Age differences in risk-taking propensity: A coordinated analysis of longitudinal panels

1. Overview of the project

How does risk-taking propensity change across the life span? We contribute to answering this question using a coordinated analysis of longitudinal panels and obtaining meta-analytic estimates of age differences in risk-taking propensity across several domains. Specifically, we report results from 12 longitudinal panels (26 samples, 187,733 unique respondents) covering general and domain-specific risk-taking propensity (financial, driving, recreational, occupational, health, social) across three or more waves spanning up to 29 years. The meta-analytic results revealed a negative relation between age and both general and domain-specific risk-taking propensity. Age differences, however, were more pronounced in specific domains, with age showing larger negative effects in the recreational and occupational domains. This work suggests there is need to understand the domain-specific nature of age differences in risk-taking propensity across the life span.

The following document contains results from all analyses conducted for the manuscript entitled “Age differences in risk-taking propensity: A coordinated analysis of longitudinal panels”. This document is organized by different domains of risk-taking propensity, including general, financial, driving, recreational, occupational, health and social domains. For each risk-taking propensity, we created 7 models, including intercept-only model (M1), fixed-effect model (M2), linear model (M3), linear with gender model (M4), linear with gender interaction model (M5), quadratic model (M6) and quadratic with gender model (M7), and provided a table summarizing individual study model results, the meta-analytic results and trajectory plots. We also tested individual predictors that are not included in the simple trajectory model in meta-regression: continent, mean age and scale range. The results from these models are available below. The code used to compile this file is available in the Github repository (https://github.com/cdsbasel/ageriskmeta).

2. Overview of panel data

2.1 Number of observations

Figure: Total number of observations by sample.

2.2 Histogram of age distributions (all observations)

Figure: Histogram of age distributions (all observations) by sample.

2.3 Histograms and density plots for every panel

This section offers a detailed overview of the different samples included in the analyses of the paper Age differences in risk-taking propensity: A coordinated analysis of longitudinal panels.

Each panel is described in a separate tab. We include the following:

Panel name: Full name of the panel.
Description: This is a general description of the objectives of the panel.
Country/Countries: Country or countries in which data are collected.
Waves: Waves available in the raw data set (not all waves were necessarily included in the data analysis as not every wave had collected data on the variables of interest)
Data collection period: Data collection period of the waves available in the raw data set.
Dataset(s) version number/name: Version number(s) or name(s) or raw dataset(s).
Data access: Link to directly access or request access to the raw dataset(s).
Age distribution: The density of each age and the number of observations in each age-bin(s).
Risk-taking propensity density: The raw score and standard Z-score risk-taking propensity density in every domain(s).

DHS

Panel Name: DNB Household Survey (DHS)

Description: The DNB Household Survey, undertaken by CentERdata at Tilburg University since 1993, provides annual financial information on 2,000 Dutch households. DNB Household Survey topics include: work, pensions, accommodation, mortgages, income, assets, liabilities, health, perception of personal financial situation and perception of risks.

More information at: https://www.eui.eu/Research/Library/ResearchGuides/Economics/Statistics/DataPortal/DNB

Country/Countries: Netherlands

Waves: 1993-2021

Data collection period: 1993-2021

Dataset(s) version number/name: NA

Data access: https://statements.centerdata.nl/

Age distribution: Left plot: density plot for age distribution; Right plot: histogram of age distributions (all observations)

Risk-taking propensity density: Left plot: density plot for raw risk-taking score; Right plot: density plot for z-transformed risk-taking score
Financial

GCOE_Japan

Panel Name: Preference Parameters Study (GCOE) Japan Sample

Description: The Preference Parameters Study of Osaka University is an extensive panel study in 4 different countries (Japan, United States, China and India). It aims to calculate parameters of preferences defining utility function; time preference, risk aversion, habit formation, externality, as well as sociodemographic characteristics. In China and India, surveys were conducted separately in urban and rural areas.

The panel survey in Japan has been conducted annually since 2003 using a random sample drawn from men and women aged 20-69 years old by a self-administered placement method. Fresh samples were selected and added in respondents to the survey for wave 2004, 2006 and 2009.

More information at: https://www.iser.osaka-u.ac.jp/survey_data/eng_panelsummary.html

Country/Countries: Japan

Waves: 2004-2010

Data collection period: 2003-2018

Dataset(s) version number/name: NA

Data access: https://www.iser.osaka-u.ac.jp/survey_data/eng_application.html

Age distribution: Left plot: density plot for age distribution; Right plot: histogram of age distributions (all observations)

Risk-taking propensity density: Left plot: density plot for raw risk-taking score; Right plot: density plot for z-transformed risk-taking score
General

GCOE_USA

Panel Name: Preference Parameters Study (GCOE) USA Sample

The panel survey for the GCOE USA sample has been conducted annually since 2005 using a random sample drawn from men and women aged 18-99 years old by a self-administered placement method. Fresh samples were selected and added in respondents to the survey for wave 2007, 2008 and 2009.

More information at: https://www.iser.osaka-u.ac.jp/survey_data/eng_panelsummary.html

Country/Countries: United States

Waves: 2005-2010

Data collection period: 2005-2013

Dataset(s) version number/name: NA

Data access: https://www.iser.osaka-u.ac.jp/survey_data/eng_application.html

Age distribution: Left plot: density plot for age distribution; Right plot: histogram of age distributions (all observations)

Risk-taking propensity density: Left plot: density plot for raw risk-taking score; Right plot: density plot for z-transformed risk-taking score
General

GLES

Panel Name: German Longitudinal Election Study

Description: The German Longitudinal Election Study (GLES) is the central survey program in Germany for the continuous collection and provision of high-quality data for national and international election research. The methodologically diverse surveys of the GLES make it possible to investigate the political attitudes and behaviour of voters and candidates. Since its foundation, the GLES has been carried out in close cooperation between the German Society for Electoral Studies (DGfW) and GESIS – Leibniz Institute for the Social Sciences.

More information at: https://gles-en.eu/

Country/Countries: Germany

Waves: wave 1-wave 15

Data collection period: 2016-2021

Dataset(s) version number/name: NA

Data access: https://search.gesis.org/research_data/ZA6838

Age distribution: Left plot: density plot for age distribution; Right plot: histogram of age distributions (all observations)

Risk-taking propensity density: Left plot: density plot for raw risk-taking score; Right plot: density plot for z-transformed risk-taking score
General

HILDA

Panel Name: Household, Income and Labour Dynamics in Australia (HILDA)

Description: The Household, Income and Labour Dynamics in Australia (HILDA) Survey is a household-based panel study that collects information about economic and personal well-being, labour market dynamics and family life of participants. Since 2001, the study has been following more than 17,000 Australian participants each year.

More information at: https://melbourneinstitute.unimelb.edu.au/hilda

Country/Countries: Australia

Waves: Wave I - Wave 19

Data collection period: 2001-present

Dataset(s) version number/name: NA

Data access: https://melbourneinstitute.unimelb.edu.au/hilda/for-data-users

Age distribution Left plot: density plot for age distribution; Right plot: histogram of age distributions (all observations)

Risk-taking propensity density: Left plot: density plot for raw risk-taking score; Right plot: density plot for z-transformed risk-taking score
Financial

HRS

Panel Name: Health and Retirement Study (HRS)

Description: The Health and Retirement Study (HRS) is a longitudinal panel study that surveys a representative sample of approximately 20,000 people in America. The target population for the first wave of the HRS was adults residing in households in the contiguous United States born between 1931 and 1941 (i.e., those who were between the ages of 51–61 in 1992 when the study began). One particular strength of the HRS sample design is the use of a steady-state sampling design: a new cohort of individuals age 51–56 is added every 6 years. Individuals and their spouses or partners are followed until their death. Data have been collected biannually since 1992.

More information at: https://hrs.isr.umich.edu/about

Country/Countries: United States

Waves: 2014-2020

Data collection period: 1984-present

Dataset(s) version number/name: Core Waves 1992-2020

Data access: https://hrsdata.isr.umich.edu/data-products/public-survey-data

Age distribution: Left plot: density plot for age distribution; Right plot: histogram of age distributions (all observations)

Risk-taking propensity density: Left plot: density plot for raw risk-taking score; Right plot: density plot for z-transformed risk-taking score
General

Driving

Financial

Recreational

Occupational

Health

LIKS

Panel Name: Life in Kyrgyzstan (LIKS)

Description: The “Life in Kyrgyzstan” Study is a longitudinal survey of households and individuals in Kyrgyzstan. It tracks the same 3,000 households and 8,000 individuals over time in all seven Kyrgyz regions (oblasts) and the two cities of Bishkek and Osh. The data are representative nationally and at the regional level (East, West, North, South). The survey interviews all adult household members about household demographics, assets, expenditure, migration, employment, agricultural markets, shocks, social networks, subjective well-being, and many other topics. Some of these topics are addressed in each wave while other topics are only addressed in selected waves. All members of the households in 2010 are tracked for each wave and new household members are added to the survey and tracked as well. The survey was first conducted in 2010 and it has been repeated four times in 2011, 2012, 2013 and 2016. The sixth wave of the LiK Study was conducted during November 2019-February 2020.

More information at: https://lifeinkyrgyzstan.org/about/

Country/Countries: Kyrgyzstan

Waves: 2010, 2011, 2012, 2013, 2016

Data collection period: 2010-present

Dataset(s) version number/name: NA

Data access: https://lifeinkyrgyzstan.org/data-access/

Age distribution: Left plot: density plot for age distribution; Right plot: histogram of age distributions (all observations)

Risk-taking propensity density: Left plot: density plot for raw risk-taking score; Right plot: density plot for z-transformed risk-taking score
General

PHF

Panel Name: Panel on Household Finances (PHF)

Description: The German Panel on Household Finances (PHF) is a panel survey on household finance and wealth in Germany, covering the balance sheet, pension, income, work life and other demographic characteristics of private households living in Germany. The first wave of the PHF was carried out in 2010/2011, the second and third wave in 2014 and 2017, respectively. In the first wave, around 3,500 randomly selected households participated, from which about 2,200 also participated in the second wave. The fourth wave was scheduled to start in spring 2021.

More information at: https://www.bundesbank.de/en/bundesbank/research/panel-on-household-finances

Country/Countries: Germany

Waves: Wave 1-Wave 3

Data collection period: 2010-present

Dataset(s) version number/name: NA

Data access: https://www.bundesbank.de/en/bundesbank/research/panel-on-household-finances/data-access-and-data-protection

Age distribution: Left plot: density plot for age distribution; Right plot: histogram of age distributions (all observations)

Risk-taking propensity density: Left plot: density plot for raw risk-taking score; Right plot: density plot for z-transformed risk-taking score
General

Financial

SAVE

Panel Name: Sparen und Altersvorsorge in Deutschland (SAVE)

Description: The Sparen und Altersvorsorge in Deutschland (SAVE) is a representative, longitudinal study on households’ financial behavior with a special focus on savings and old-age provision. SAVE collected data on households’ financial structure and relevant socio- and psychological aspects between 2001 and 2013.

More information at: https://www.mpisoc.mpg.de/en/social-policy-mea/research/save-2001-2013/

Country/Countries: Germany

Waves: 2001-2013

Data collection period: 2001-2013

Dataset(s) version number/name: NA

Data access: https://dbk.gesis.org/dbksearch/GDESC2.asp?no=0014&search=save&search2=&DB=d&tab=0&notabs=&nf=1&af=&ll=10

Age distribution: Left plot: density plot for age distribution; Right plot: histogram of age distributions (all observations)

Risk-taking propensity density: Left plot: density plot for raw risk-taking score; Right plot: density plot for z-transformed risk-taking score
Driving

Financial

Recreational

Occupational

Health

SHARE_Austria

Panel Name: Survey of Health, Ageing and Retirement in Europe (SHARE) Austria Sample

Description: The Survey of Health, Ageing and Retirement in Europe (SHARE) is a research infrastructure for studying the effects of health, social, economic and environmental policies over the life-course of European citizens and beyond. From 2004 until today, 140,000 people aged 50 or older from 28 European countries and Israel have been interviewed in 7 waves. SHARE is the largest pan-European social science panel study providing internationally comparable longitudinal micro data that allow insights in the fields of public health and socioeconomic living conditions of European individuals.

More information at: http://www.share-project.org/home0.html

Country/Countries: Austria

Waves: 2007, 2011, 2013, 2015, 2017, 2019

Data collection period: 2007, 2011, 2013, 2015, 2017, 2019

Dataset(s) version number/name: NA

Data access: http://www.share-project.org/data-access.html

Age distribution: Left plot: density plot for age distribution; Right plot: histogram of age distributions (all observations)

Risk-taking propensity density: Left plot: density plot for raw risk-taking score; Right plot: density plot for z-transformed risk-taking score
Financial

SHARE_Belgium

Panel Name: Survey of Health, Ageing and Retirement in Europe (SHARE) Belgium Sample

More information at: http://www.share-project.org/home0.html

Country/Countries: Belgium

Waves: 2007, 2011, 2013, 2015, 2017, 2019

Data collection period: 2007, 2011, 2013, 2015, 2017, 2019

Dataset(s) version number/name: NA

Data access: http://www.share-project.org/data-access.html

Age distribution: Left plot: density plot for age distribution; Right plot: histogram of age distributions (all observations)

Risk-taking propensity density: Left plot: density plot for raw risk-taking score; Right plot: density plot for z-transformed risk-taking score
Financial

SHARE_Czech_Republic

Panel Name: Survey of Health, Ageing and Retirement in Europe (SHARE) Czech Republic Sample

More information at: http://www.share-project.org/home0.html

Country/Countries: Czech Republic

Waves: 2007, 2011, 2013, 2015, 2017

Data collection period: 2007, 2011, 2013, 2015, 2017, 2019

Dataset(s) version number/name: NA

Data access: http://www.share-project.org/data-access.html

Age distribution: Left plot: density plot for age distribution; Right plot: histogram of age distributions (all observations)

Risk-taking propensity density: Left plot: density plot for raw risk-taking score; Right plot: density plot for z-transformed risk-taking score
Financial

SHARE_Denmark

Panel Name: Survey of Health, Ageing and Retirement in Europe (SHARE) Denmark Sample

More information at: http://www.share-project.org/home0.html

Country/Countries: Denmark

Waves: 2007, 2011, 2013, 2015, 2017

Data collection period: 2007, 2011, 2013, 2015, 2017, 2019

Dataset(s) version number/name: NA

Data access: http://www.share-project.org/data-access.html

Age distribution: Left plot: density plot for age distribution; Right plot: histogram of age distributions (all observations)

Risk-taking propensity density: Left plot: density plot for raw risk-taking score; Right plot: density plot for z-transformed risk-taking score
Financial

SHARE_Estonia

Panel Name: Survey of Health, Ageing and Retirement in Europe (SHARE) Estonia Sample

More information at: http://www.share-project.org/home0.html

Country/Countries: Estonia

Waves: 2011, 2013, 2015

Data collection period: 2011, 2013, 2015, 2019

Dataset(s) version number/name: NA

Data access: http://www.share-project.org/data-access.html

Age distribution: Left plot: density plot for age distribution; Right plot: histogram of age distributions (all observations)

Risk-taking propensity density: Left plot: density plot for raw risk-taking score; Right plot: density plot for z-transformed risk-taking score
Financial

SHARE_France

Panel Name: Survey of Health, Ageing and Retirement in Europe (SHARE) France Sample

Description: TThe Survey of Health, Ageing and Retirement in Europe (SHARE) is a research infrastructure for studying the effects of health, social, economic and environmental policies over the life-course of European citizens and beyond. From 2004 until today, 140,000 people aged 50 or older from 28 European countries and Israel have been interviewed in 7 waves. SHARE is the largest pan-European social science panel study providing internationally comparable longitudinal micro data that allow insights in the fields of public health and socioeconomic living conditions of European individuals.

More information at: http://www.share-project.org/home0.html

Country/Countries: France

Waves: 2007, 2011, 2013, 2015, 2017

Data collection period: 2007, 2011, 2013, 2015, 2017, 2019

Dataset(s) version number/name: NA

Data access: http://www.share-project.org/data-access.html

Age distribution: Left plot: density plot for age distribution; Right plot: histogram of age distributions (all observations)

Risk-taking propensity density: Left plot: density plot for raw risk-taking score; Right plot: density plot for z-transformed risk-taking score
Financial

SHARE_Germany

Panel Name: Survey of Health, Ageing and Retirement in Europe (SHARE) Germany Sample

More information at: http://www.share-project.org/home0.html

Country/Countries: Germany

Waves: 2007, 2011, 2013, 2015, 2017, 2019

Data collection period: 2007, 2011, 2013, 2015, 2017, 2019

Dataset(s) version number/name: NA

Data access: http://www.share-project.org/data-access.html

Age distribution: Left plot: density plot for age distribution; Right plot: histogram of age distributions (all observations)

Risk-taking propensity density: Left plot: density plot for raw risk-taking score; Right plot: density plot for z-transformed risk-taking score
Financial

SHARE_Israel

Panel Name: Survey of Health, Ageing and Retirement in Europe (SHARE) Israel Sample

More information at: http://www.share-project.org/home0.html

Country/Countries: Israel

Waves: 2007, 2013, 2015

Data collection period: 2007, 2013, 2015, 2019

Dataset(s) version number/name: NA

Data access: http://www.share-project.org/data-access.html

Age distribution: Left plot: density plot for age distribution; Right plot: histogram of age distributions (all observations)

Risk-taking propensity density: Left plot: density plot for raw risk-taking score; Right plot: density plot for z-transformed risk-taking score
Financial

SHARE_Italy

Panel Name: Survey of Health, Ageing and Retirement in Europe (SHARE) Italy Sample

More information at: http://www.share-project.org/home0.html

Country/Countries: Italy

Waves: 2007, 2011, 2013, 2015, 2017, 2019

Data collection period: 2007, 2011, 2013, 2015, 2017, 2019

Dataset(s) version number/name: NA

Data access: http://www.share-project.org/data-access.html

Age distribution: Left plot: density plot for age distribution; Right plot: histogram of age distributions (all observations)

Risk-taking propensity density: Left plot: density plot for raw risk-taking score; Right plot: density plot for z-transformed risk-taking score
Financial

SHARE_Netherlands

Panel Name: Survey of Health, Ageing and Retirement in Europe (SHARE) Netherlands Sample

More information at: http://www.share-project.org/home0.html

Country/Countries: Netherlands

Waves: 2007, 2011, 2013, 2019

Data collection period: 2007, 2011, 2013, 2019

Dataset(s) version number/name: NA

Data access: http://www.share-project.org/data-access.html

Age distribution: Left plot: density plot for age distribution; Right plot: histogram of age distributions (all observations)

Risk-taking propensity density: Left plot: density plot for raw risk-taking score; Right plot: density plot for z-transformed risk-taking score
Financial

SHARE_Slovenia

Panel Name: Survey of Health, Ageing and Retirement in Europe (SHARE) Slovenia Sample

More information at: http://www.share-project.org/home0.html

Country/Countries: Slovenia

Waves: 2011, 2013, 2015, 2019

Data collection period: 2011, 2013, 2015, 2019

Dataset(s) version number/name: NA

Data access: http://www.share-project.org/data-access.html

Age distribution: Left plot: density plot for age distribution; Right plot: histogram of age distributions (all observations)

Risk-taking propensity density: Left plot: density plot for raw risk-taking score; Right plot: density plot for z-transformed risk-taking score
Financial

SHARE_Spain

Panel Name: Survey of Health, Ageing and Retirement in Europe (SHARE) Spain Sample

More information at: http://www.share-project.org/home0.html

Country/Countries: Spain

Waves: 2007, 2011, 2013, 2015, 2017

Data collection period: 2007, 2011, 2013, 2015, 2017, 2019

Dataset(s) version number/name: NA

Data access: http://www.share-project.org/data-access.html

Age distribution: Left plot: density plot for age distribution; Right plot: histogram of age distributions (all observations)

Risk-taking propensity density: Left plot: density plot for raw risk-taking score; Right plot: density plot for z-transformed risk-taking score
Financial

SHARE_Sweden

Panel Name: Survey of Health, Ageing and Retirement in Europe (SHARE) Sweden Sample

More information at: http://www.share-project.org/home0.html

Country/Countries: Sweden

Waves: 2007, 2011, 2013, 2015, 2017

Data collection period: 2007, 2011, 2013, 2015, 2017, 2019

Dataset(s) version number/name: NA

Data access: http://www.share-project.org/data-access.html

Age distribution: Left plot: density plot for age distribution; Right plot: histogram of age distributions (all observations)

Risk-taking propensity density: Left plot: density plot for raw risk-taking score; Right plot: density plot for z-transformed risk-taking score
Financial

SHARE_Switzerland

Panel Name: Survey of Health, Ageing and Retirement in Europe (SHARE) Switzerland Sample

More information at: http://www.share-project.org/home0.html

Country/Countries: Switzerland

Waves: 2007, 2011, 2013, 2015, 2017, 2019

Data collection period: 2007, 2011, 2013, 2015, 2017, 2019

Dataset(s) version number/name: NA

Data access: http://www.share-project.org/data-access.html

Age distribution: Left plot: density plot for age distribution; Right plot: histogram of age distributions (all observations)

Risk-taking propensity density: Left plot: density plot for raw risk-taking score; Right plot: density plot for z-transformed risk-taking score
Financial

SOEP

Panel Name: German Socio-Economic Panel (SOEP)

Description: The Socio-Economic Panel (SOEP) is one of the largest and longest-running multidisciplinary household surveys worldwide. Every year, approximately 30,000 people in 15,000 households are interviewed for the SOEP study. The SOEP is also a research-driven infrastructure based at DIW Berlin. The SOEP team prepares survey data for use by researchers around the globe, and team members use the data in research on various topics. Studies based on SOEP data examine diverse aspects of societal change.

More information at: https://www.diw.de/en/diw_01.c.600489.en/about_us.html#c_624242

Country/Countries: Germany

Waves: 2004-2019

Data collection period: 1984-present

Dataset(s) version number/name: SOEP-Core v36

Data access: https://www.diw.de/sixcms/detail.php?id=diw_01.c.814095.en

Age distribution: Left plot: density plot for age distribution; Right plot: histogram of age distributions (all observations)

UAS

Panel Name: Understanding America Study

Description: The Understanding America Study (UAS) is a panel of households at the University of Southern California (USC) of approximately 9,500 respondents representing the entire United States. The study is an ‘Internet Panel,’ which means that respondents answer our surveys on a computer, tablet, or smart phone, wherever they are and whenever they wish to participate.

More information at: https://uasdata.usc.edu/index.php

Country/Countries: United States

Waves: wave 1-wave 4

Data collection period: 2015-2021

Dataset(s) version number/name: NA

Data access: https://uasdata.usc.edu/index.php

Age distribution: Left plot: density plot for age distribution; Right plot: histogram of age distributions (all observations)

Risk-taking propensity density: Left plot: density plot for raw risk-taking score; Right plot: density plot for z-transformed risk-taking score
General

USoc

Panel Name: UK Household Longitudinal Survey (Understanding Society) (USoc)

Description: The UK Household Longitudinal Study/Understanding Society (USoc) is built on the British Household Panel Survey (BHPS), which ran from 1991-2009 and had around 10,000 households in it. Understanding Society started in 2009 and interviewed around 40,000 households, including around 8,000 of the original BHPS households.The USoc examines how life in the UK is changing and what stays the same over many years and includes questions on various topics including social, economic and behavioral factors. Interviews are held with each member of the household in order to examine how different generations experience life in the UK.

More information at: https://www.understandingsociety.ac.uk/about/about-the-study

Country/Countries: United Kingdom

Waves: 2008, 2013, 2014

Data collection period: Waves 1-11, 2008-2018

Dataset(s) version number/name: Understanding Society: Innovation Panel

Data access: https://www.understandingsociety.ac.uk/documentation/access-data

Age distribution: Left plot: density plot for age distribution; Right plot: histogram of age distributions (all observations)

Risk-taking propensity density: Left plot: density plot for raw risk-taking score; Right plot: density plot for z-transformed risk-taking score
General

3. Multilevel model process

This section offers a detailed overview of the 7 different models included in the multilevel analysis in the paper Age differences in risk-taking propensity: A coordinated analysis of longitudinal panels.

Each model is described in a separate tab. We include the following:

Model name: General name of model
Description: This is a general description of the model, including some details of the model
Analysis: The code to run in R and interpret the model, along with the annotations the meaning of each part of the code.

Intercept-only model

Model name: Intercept-only model, also called unconditional model.
Description: In the unconditional model, only the dependent variable and the grouping variable(s) (e.g., subject ID) are entered. No predictors are entered thus the model is not “conditioned” upon any predictor variables. This intercept-only model is the first step in conducting multilevel modeling, aiming to make sure mutlilevel modeling is appropriate in the first place.
Analysis: Model <- lmer (risk ~ 1 + (1|subject), data = DATA)
- Model: Tells R to save the output of the analyses to an object called “Model”.
- lmer: This is the command to test a mixed linear model using lme4.
- risk ~ 1: Specifies an unconditional model in the form DV~IV. When there are no predictors, 1 is entered in the IV’s place. In our model, risk is the DV, representing the risk-taking propensity.
- 1|subject: Specifies that level-1 observations are grouped by the level-2 variable called “subject”, representing the subjects’ ID number.
- data = DATA: Specifies that the variables (e.g., risk, subject ID) are in a dataset called “DATA”.

Fixed-effect model

Model name: Fixed-effect model, also called age fixed-effect model.
Description: After determining that a multilevel model is appropriate, the next step is to begin to add level-1 predictors. Within multilevel modeling of real-time monitoring data, level-1 is almost always the “observation” level. In our analysis, the level one predictor is “age”. In the fixed-effect model, we regard age as a predictor but did not consider differences across participants, so called fixed-effect model.
Analysis: Model <- lmer (risk ~ age + (1|subject), data = DATA)
- Model: Tells R to save the output of the analyses to an object called “Model”.
- lmer: This is the command to test a mixed linear model using lme4.
- risk ~ age: Formula that lme4 will process, specified in the form DV~IV. In our model, age is not the raw age. We centered the age variable to a reference age (50 years old) and standardized the age variable to decades by dividing it by 10, then use the transformed age in our model.
- 1|subject: Specifies that level-1 observations are grouped by the level-2 variable called “subject”, representing the subjects’ ID number.
- data = DATA: Specifies that the variables (e.g., risk, subject ID) are in a dataset called “DATA”.

Linear model

Model name: Linear model, also called age fixed- and random-effects model effects model
Description: In the linear model, we regard age as a predictor and also include differences across participants, so in turn, this model included age both as a fixed and a random slope.
Analysis: Model <- lmer (risk ~ age + (1+age|subject), data = DATA)
- Model: Tells R to save the output of the analyses to an object called “Model”
- lmer: This is the command to test a mixed linear model using lme4.
- risk ~ age: Formula that lme4 will process, specified in the form DV~IV, the independent variable in the model is centered and standardized age.
- 1+age|subject: Specifies that the model include not only age fixed effect, but also age random effect.
- data = DATA: Specifies that the variables (e.g., risk, age, subject ID) are in a dataset called “DATA”

Linear with gender model

Model name: Linear with gender model, also called age fixed- and random-effects effects model with gender
Description: The next step involves entering level-2 effects, although it is not always necessary to take this piecewise approach testing a level-1-effects-only model first. A model with level-2 variables should only be used when the theoretical conceptualization of the model necessitates it and there is sufficient power to do so. In this model, we are interested in adjusting for the effect of gender, so enter gender as a level-2 predictor. In this way, we coded the relation between inter-individual differences in the change trajectories and the time-invariant characteristic (gender) of the individual to compare whether age is associated with risk-taking propensity in males and females in same manner.
Analysis: Model <- lmer (risk ~ age + gender + (1+age|subject), data = DATA)
- Model: Tells R to save the output of the analyses to an object called “Model”.
- lmer: This is the command to test a mixed linear model using lme4.
- risk ~ age + gender: Formula that lme4 will process, specified in the form DV~IV1+IV2, the first independent variable in the model is level-1 predictor (i.e., centered and standardized age), and the second independent variable in the model is level-2 predictor(i.e.,gender).
- 1+age|subject: Specifies that the model include not only age fixed effect, but also age random effect.
- data = DATA: Specifies that the variables (e.g., risk, age, gender, subject ID) are in a dataset called “DATA”

Linear with gender interaction model

Model name: Linear with gender interaction model, also called age fixed- and random- effects model with gender, including an age by gender interaction
Description: This model further included an age by gender interaction based on previous model.
Analysis: Model <- lmer (risk ~ age + age$\times$gender + (1+age|subject), data = DATA)
- Model: Tells R to save the output of the analyses to an object called “Model”
- lmer: This is the command to test a mixed linear model using lme4.
- risk ~ age + age$\times$gender: Formula that lme4 will process, specified in the form DV~IV1+IV2, the first independent variable in the model is level-1 predictor (i.e., centered and standardized age), and the second independent variable in the model is the interaction between age and gender.
- 1+age|subject: Specifies that the model include not only age fixed effect, but also age random effect.
- data = DATA: Specifies that the variables (e.g., risk, age, gender, subject ID) are in a dataset called “DATA”

Quadratic model

Model name: Quadratic model, also called age quadratic growth model
Description: we fit quadratic growth models to assess non-linear change. We did this by squaring age variable and entering this into a model.
Analysis: Model <- lmer (risk ~ age + I($age^2$) + (1+age|subject), data = DATA)
- Model: Tells R to save the output of the analyses to an object called “Model”
- lmer: This is the command to test a mixed linear model using lme4.
- risk ~ age + I($age^2$): Formula that lme4 will process, specified in the form DV~IV1+IV2, the first independent variable in the model is level-1 predictor (i.e., centered and standardized age), and the second independent variable in the model is quadratic age.
- 1+age|subject: Specifies that the model include not only age fixed effect, but also age random effect.
- data = DATA: Specifies that the variables (e.g., risk, subject ID) are in a dataset called “DATA”

Quadratic with gender model

Model name: Quadratic with gender model, also called age quadratic growth model with gender.
Description: We added gender variable into quadratic growth model to assess potential age differences in the quadratic trajectories.
Analysis: Model <- lmer (risk ~ age + I($age^2$) + gender + (1+age|subject), data = DATA)
- Model: Tells R to save the output of the analyses to an object called “Model”
- lmer: This is the command to test a mixed linear model using lme4.
- risk ~ age + I($age^2$) + gender: Formula that lme4 will process, specified in the form DV~IV1+IV2+IV3, the first independent variable in the model is level-1 predictor (i.e., centered and standardized age), the second independent variable in the model is quadratic age, and the third independent variable in the model is level-2 predictor (i.e.,gender).
- 1+age|subject: Specifies that the model include not only age fixed effect, but also age random effect.
- data = DATA: Specifies that the variables (e.g., risk, subject ID) are in a dataset called “DATA”

4. Multilevel model results

4.1. General risk-taking

Intercept only model

Models results:

Fixed effect model

Models results:

Linear model

Models results:

Plot age trajectory:

Figure: Age trajectories of general risk-taking propensity for each sample. The points represent moving average (window size = 5, window step = 2) of raw data. The lines represent the age trajectory of linear model results.

Linear with gender model

Models results:

Plot age trajectory:

Figure: Age trajectories of general risk-taking propensity for each sample. The points represent moving average (window size = 5, window step = 2) of raw data. Circle = female, triangle = male. The lines represent the age trajectory of linear with gender model results. Solid line = female, dotted line = male.

Linear with gender interaction model

Models results:

Plot age trajectory:

Figure: Age trajectories of general risk-taking propensity for each sample. The points represent moving average (window size = 5, window step = 2) of raw data. Circle = female, triangle = male. The lines represent the age trajectory of linear with gender interaction model results. Solid line = female, dotted line = male.

Quadratic model

Models results:

Plot age trajectory:

Quadratic with gender model

Models results:

Plot age trajectory:

Figure: Age trajectories of general risk-taking propensity for each sample. The points represent moving average (window size = 5, window step = 2) of raw data. Circle = female, triangle = male. The lines represent the age trajectory of quadratic with gender model results. Solid line = female, dotted line = male.

4.2. Financial risk-taking

Intercept only model

Models results:

Fixed effect model

Models results:

Linear model

Models results:

Plot age trajectory:

Figure: Age trajectories of financial risk-taking propensity for each sample. The points represent moving average (window size = 5, window step = 2) of raw data. The lines represent the age trajectory of linear model results.

Linear with gender model

Models results:

Plot age trajectory:

$Figure: Age trajectories of financial risk-taking propensity for each sample. The points represent moving average (window size = 5, window step = 2) of raw data. Circle = female, triangle = male. The lines represent the age trajectory of linear with gender model results. Solid line = female, dotted line = male.$

Figure: Age trajectories of financial risk-taking propensity for each sample. The points represent moving average (window size = 5, window step = 2) of raw data. Circle = female, triangle = male. The lines represent the age trajectory of linear with gender model results. Solid line = female, dotted line = male.

Linear with gender interaction model

Models results:

Plot age trajectory:

$Figure: Age trajectories of financial risk-taking propensity for each sample. The points represent moving average (window size = 5, window step = 2) of raw data. Circle = female, triangle = male. The lines represent the age trajectory of linear with gender interaction model results. Solid line = female, dotted line = male.$

Figure: Age trajectories of financial risk-taking propensity for each sample. The points represent moving average (window size = 5, window step = 2) of raw data. Circle = female, triangle = male. The lines represent the age trajectory of linear with gender interaction model results. Solid line = female, dotted line = male.

Quadratic model

Models results:

Plot age trajectory:

Quadratic with gender model

Models results:

Plot age trajectory:

Figure: Age trajectories of financial risk-taking propensity for each sample. The points represent moving average (window size = 5, window step = 2) of raw data. Circle = female, triangle = male. The lines represent the age trajectory of quadratic with gender model results. Solid line = female, dotted line = male.

4.3. Driving risk-taking

Intercept only model

Models results:

Fixed effect model

Models results:

Linear model

Models results:

Plot age trajectory:

Figure: Age trajectories of driving risk-taking propensity for each sample. The points represent moving average (window size = 5, window step = 2) of raw data. The lines represent the age trajectory of linear model results.

Linear with gender model

Models results:

Plot age trajectory:

Figure: Age trajectories of driving risk-taking propensity for each sample. The points represent moving average (window size = 5, window step = 2) of raw data. Circle = female, triangle = male. The lines represent the age trajectory of linear with gender model results. Solid line = female, dotted line = male.

Linear with gender interaction model

Models results:

Plot age trajectory:

Figure: Age trajectories of driving risk-taking propensity for each sample. The points represent moving average (window size = 5, window step = 2) of raw data. Circle = female, triangle = male. The lines represent the age trajectory of linear with gender interation model results. Solid line = female, dotted line = male.

Quadratic model

Models results:

Plot age trajectory:

Quadratic with gender model

Models results:

Plot age trajectory:

Figure: Age trajectories of driving risk-taking propensity for each sample. The points represent moving average (window size = 5, window step = 2) of raw data. Circle = female, triangle = male. The lines represent the age trajectory of quadratic with gender model results. Solid line = female, dotted line = male.

4.4. Recreational risk-taking

Intercept only model

Models results:

Fixed effect model

Models results:

Linear model

Models results:

Plot age trajectory:

Figure: Age trajectories of recreational risk-taking propensity for each sample. The points represent moving average (window size = 5, window step = 2) of raw data. The lines represent the age trajectory of linear model results.

Linear with gender model

Models results:

Plot age trajectory:

Figure: Age trajectories of recreational risk-taking propensity for each sample. The points represent moving average (window size = 5, window step = 2) of raw data. Circle = female, triangle = male. The lines represent the age trajectory of linear with gender model results. Solid line = female, dotted line = male.

Linear with gender interaction model

Models results:

Plot age trajectory:

Figure: Age trajectories of recreational risk-taking propensity for each sample. The points represent moving average (window size = 5, window step = 2) of raw data. Circle = female, triangle = male. The lines represent the age trajectory of linear with gender interaction model results. Solid line = female, dotted line = male.

Quadratic model

Models results:

Plot age trajectory:

Quadratic with gender model

Models results:

Plot age trajectory:

Figure: Age trajectories of recreational risk-taking propensity for each sample. The points represent moving average (window size = 5, window step = 2) of raw data. Circle = female, triangle = male. The lines represent the age trajectory of quadratic with gender model results. Solid line = female, dotted line = male.

4.5. Occupational risk-taking

Intercept only model

Models results:

Fixed effect model

Models results:

Linear model

Models results:

Plot age trajectory:

Figure: Age trajectories of occupational risk-taking propensity for each sample. The points represent moving average (window size = 5, window step = 2) of raw data. The lines represent the age trajectory of linear model results.

Linear with gender model

Models results:

Plot age trajectory:

Figure: Age trajectories of occupational risk-taking propensity for each sample. The points represent moving average (window size = 5, window step = 2) of raw data. Circle = female, triangle = male. The lines represent the age trajectory of linear with gender model results. Solid line = female, dotted line = male.

Linear with gender interaction model

Models results:

Plot age trajectory:

Figure: Age trajectories of occupational risk-taking propensity for each sample. The points represent moving average (window size = 5, window step = 2) of raw data. Circle = female, triangle = male. The lines represent the age trajectory of linear with gender interaction model results. Solid line = female, dotted line = male.

Quadratic model

Models results:

Plot age trajectory:

Quadratic with gender model

Models results:

Plot age trajectory:

Figure: Age trajectories of occupational risk-taking propensity for each sample. The points represent moving average (window size = 5, window step = 2) of raw data. Circle = female, triangle = male. The lines represent the age trajectory of quadratic with gender model results. Solid line = female, dotted line = male.

4.6. Health risk-taking

Intercept only model

Models results:

Fixed effect model

Models results:

Linear model

Models results:

Plot age trajectory:

Figure: Age trajectories of health risk-taking propensity for each sample. The points represent moving average (window size = 5, window step = 2) of raw data. The lines represent the age trajectory of linear model results.

Linear with gender model

Models results:

Plot age trajectory:

Figure: Age trajectories of health risk-taking propensity for each sample. The points represent moving average (window size = 5, window step = 2) of raw data. Circle = female, triangle = male. The lines represent the age trajectory of linear with gender model results. Solid line = female, dotted line = male.

Linear with gender interaction model

Models results:

Plot age trajectory:

Figure: Age trajectories of health risk-taking propensity for each sample. The points represent moving average (window size = 5, window step = 2) of raw data. Circle = female, triangle = male. The lines represent the age trajectory of linear with gender interaction model results. Solid line = female, dotted line = male.

Quadratic model

Models results:

Plot age trajectory:

Quadratic with gender model

Models results:

Plot age trajectory:

Figure: Age trajectories of health risk-taking propensity for each sample. The points represent moving average (window size = 5, window step = 2) of raw data. Circle = female, triangle = male. The lines represent the age trajectory of quadratic with gender model results. Solid line = female, dotted line = male.

5. Meta-analysis results

5.1. General risk-taking

Intercept only model

Meta analysis:
ICC’s results

## 
## Random-Effects Model (k = 9; tau^2 estimator: REML)
## 
##   logLik  deviance       AIC       BIC      AICc 
##   4.8613   -9.7226   -5.7226   -5.5637   -3.3226   
## 
## tau^2 (estimated amount of total heterogeneity): 0.0173 (SE = 0.0087)
## tau (square root of estimated tau^2 value):      0.1317
## I^2 (total heterogeneity / total variability):   99.89%
## H^2 (total variability / sampling variability):  917.75
## 
## Test for Heterogeneity:
## Q(df = 8) = 7220.3611, p-val < .0001
## 
## Model Results:
## 
## estimate      se     zval    pval   ci.lb   ci.ub 
##   0.4611  0.0440  10.4799  <.0001  0.3748  0.5473  *** 
## 
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

Meta analysis with three moderators (continent, mean age, scale range):
ICC’s results

## 
## Mixed-Effects Model (k = 9; tau^2 estimator: REML)
## 
##   logLik  deviance       AIC       BIC      AICc 
##   3.9228   -7.8456    2.1544    0.2016   62.1544   
## 
## tau^2 (estimated amount of residual heterogeneity):     0.0121 (SE = 0.0077)
## tau (square root of estimated tau^2 value):             0.1101
## I^2 (residual heterogeneity / unaccounted variability): 99.82%
## H^2 (unaccounted variability / sampling variability):   553.34
## R^2 (amount of heterogeneity accounted for):            30.12%
## 
## Test for Residual Heterogeneity:
## QE(df = 5) = 2371.6040, p-val < .0001
## 
## Test of Moderators (coefficients 2:4):
## QM(df = 3) = 6.4145, p-val = 0.0931
## 
## Model Results:
## 
##                         estimate      se     zval    pval    ci.lb   ci.ub 
## intrcpt                  -0.0039  0.3209  -0.0121  0.9903  -0.6328  0.6250    
## continentEurope           0.1707  0.1035   1.6491  0.0991  -0.0322  0.3737  . 
## continentNorth America    0.0322  0.1201   0.2678  0.7888  -0.2033  0.2676    
## mean.age                  0.0073  0.0068   1.0794  0.2804  -0.0060  0.0206    
## 
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

Note: Scale range was not included as a moderator in the meta-analysis results because all samples used the same measure scale of general risk-taking propensity

Fixed effect model

Meta analysis:
Age effect results

## 
## Random-Effects Model (k = 9; tau^2 estimator: REML)
## 
##   logLik  deviance       AIC       BIC      AICc 
##  14.4883  -28.9767  -24.9767  -24.8178  -22.5767   
## 
## tau^2 (estimated amount of total heterogeneity): 0.0014 (SE = 0.0007)
## tau (square root of estimated tau^2 value):      0.0372
## I^2 (total heterogeneity / total variability):   98.28%
## H^2 (total variability / sampling variability):  58.08
## 
## Test for Heterogeneity:
## Q(df = 8) = 282.2381, p-val < .0001
## 
## Model Results:
## 
## estimate      se     zval    pval    ci.lb    ci.ub 
##  -0.0745  0.0127  -5.8718  <.0001  -0.0994  -0.0496  *** 
## 
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

Meta analysis with three moderators (continent, mean age, scale range):
Age effect results

## 
## Mixed-Effects Model (k = 9; tau^2 estimator: REML)
## 
##   logLik  deviance       AIC       BIC      AICc 
##   9.1819  -18.3638   -8.3638  -10.3166   51.6362   
## 
## tau^2 (estimated amount of residual heterogeneity):     0.0013 (SE = 0.0009)
## tau (square root of estimated tau^2 value):             0.0364
## I^2 (residual heterogeneity / unaccounted variability): 97.51%
## H^2 (unaccounted variability / sampling variability):   40.12
## R^2 (amount of heterogeneity accounted for):            3.82%
## 
## Test for Residual Heterogeneity:
## QE(df = 5) = 124.9845, p-val < .0001
## 
## Test of Moderators (coefficients 2:4):
## QM(df = 3) = 3.6443, p-val = 0.3025
## 
## Model Results:
## 
##                         estimate      se     zval    pval    ci.lb   ci.ub 
## intrcpt                  -0.0544  0.1072  -0.5074  0.6119  -0.2646  0.1557    
## continentEurope          -0.0176  0.0350  -0.5032  0.6149  -0.0862  0.0510    
## continentNorth America    0.0383  0.0403   0.9506  0.3418  -0.0406  0.1172    
## mean.age                 -0.0005  0.0023  -0.2179  0.8275  -0.0049  0.0039    
## 
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

Note: Scale range was not included as a moderator in the meta-analysis results because all samples used the same measure scale of general risk-taking propensity

Linear model

Meta analysis:
Age effect results

## 
## Random-Effects Model (k = 9; tau^2 estimator: REML)
## 
##   logLik  deviance       AIC       BIC      AICc 
##  14.5789  -29.1578  -25.1578  -24.9989  -22.7578   
## 
## tau^2 (estimated amount of total heterogeneity): 0.0013 (SE = 0.0007)
## tau (square root of estimated tau^2 value):      0.0366
## I^2 (total heterogeneity / total variability):   98.19%
## H^2 (total variability / sampling variability):  55.30
## 
## Test for Heterogeneity:
## Q(df = 8) = 262.8493, p-val < .0001
## 
## Model Results:
## 
## estimate      se     zval    pval    ci.lb    ci.ub 
##  -0.0743  0.0125  -5.9356  <.0001  -0.0988  -0.0498  *** 
## 
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

Meta analysis with three moderators (continent, mean age, scale range):
Age effect results

## 
## Mixed-Effects Model (k = 9; tau^2 estimator: REML)
## 
##   logLik  deviance       AIC       BIC      AICc 
##   9.2063  -18.4127   -8.4127  -10.3655   51.5873   
## 
## tau^2 (estimated amount of residual heterogeneity):     0.0013 (SE = 0.0009)
## tau (square root of estimated tau^2 value):             0.0361
## I^2 (residual heterogeneity / unaccounted variability): 97.47%
## H^2 (unaccounted variability / sampling variability):   39.59
## R^2 (amount of heterogeneity accounted for):            2.61%
## 
## Test for Residual Heterogeneity:
## QE(df = 5) = 119.7080, p-val < .0001
## 
## Test of Moderators (coefficients 2:4):
## QM(df = 3) = 3.5562, p-val = 0.3135
## 
## Model Results:
## 
##                         estimate      se     zval    pval    ci.lb   ci.ub 
## intrcpt                  -0.0579  0.1064  -0.5447  0.5860  -0.2665  0.1506    
## continentEurope          -0.0162  0.0347  -0.4668  0.6407  -0.0842  0.0518    
## continentNorth America    0.0383  0.0400   0.9598  0.3372  -0.0400  0.1166    
## mean.age                 -0.0004  0.0022  -0.1927  0.8472  -0.0048  0.0040    
## 
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

Note: Scale range was not included as a moderator in the meta-analysis results because all samples used the same measure scale of general risk-taking propensity

Linear with gender model

Meta analysis:
Age effect results

## 
## Random-Effects Model (k = 9; tau^2 estimator: REML)
## 
##   logLik  deviance       AIC       BIC      AICc 
##  14.5510  -29.1019  -25.1019  -24.9431  -22.7019   
## 
## tau^2 (estimated amount of total heterogeneity): 0.0014 (SE = 0.0007)
## tau (square root of estimated tau^2 value):      0.0368
## I^2 (total heterogeneity / total variability):   98.26%
## H^2 (total variability / sampling variability):  57.35
## 
## Test for Heterogeneity:
## Q(df = 8) = 254.0023, p-val < .0001
## 
## Model Results:
## 
## estimate      se     zval    pval    ci.lb    ci.ub 
##  -0.0762  0.0126  -6.0688  <.0001  -0.1008  -0.0516  *** 
## 
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

Gender effect results

## 
## Random-Effects Model (k = 9; tau^2 estimator: REML)
## 
##   logLik  deviance       AIC       BIC      AICc 
##   6.6990  -13.3980   -9.3980   -9.2391   -6.9980   
## 
## tau^2 (estimated amount of total heterogeneity): 0.0105 (SE = 0.0056)
## tau (square root of estimated tau^2 value):      0.1026
## I^2 (total heterogeneity / total variability):   97.93%
## H^2 (total variability / sampling variability):  48.28
## 
## Test for Heterogeneity:
## Q(df = 8) = 311.5390, p-val < .0001
## 
## Model Results:
## 
## estimate      se     zval    pval    ci.lb    ci.ub 
##  -0.2550  0.0353  -7.2306  <.0001  -0.3241  -0.1859  *** 
## 
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

Meta analysis with three moderators (continent, mean age, scale range):
Age effect results

## 
## Mixed-Effects Model (k = 9; tau^2 estimator: REML)
## 
##   logLik  deviance       AIC       BIC      AICc 
##   9.1590  -18.3181   -8.3181  -10.2709   51.6819   
## 
## tau^2 (estimated amount of residual heterogeneity):     0.0013 (SE = 0.0009)
## tau (square root of estimated tau^2 value):             0.0365
## I^2 (residual heterogeneity / unaccounted variability): 97.58%
## H^2 (unaccounted variability / sampling variability):   41.30
## R^2 (amount of heterogeneity accounted for):            1.34%
## 
## Test for Residual Heterogeneity:
## QE(df = 5) = 118.6911, p-val < .0001
## 
## Test of Moderators (coefficients 2:4):
## QM(df = 3) = 3.4554, p-val = 0.3266
## 
## Model Results:
## 
##                         estimate      se     zval    pval    ci.lb   ci.ub 
## intrcpt                  -0.0616  0.1075  -0.5732  0.5665  -0.2723  0.1491    
## continentEurope          -0.0159  0.0350  -0.4538  0.6500  -0.0846  0.0528    
## continentNorth America    0.0383  0.0404   0.9489  0.3427  -0.0408  0.1174    
## mean.age                 -0.0004  0.0023  -0.1769  0.8596  -0.0049  0.0040    
## 
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

Gender effect results

## 
## Mixed-Effects Model (k = 9; tau^2 estimator: REML)
## 
##   logLik  deviance       AIC       BIC      AICc 
##   3.9319   -7.8638    2.1362    0.1834   62.1362   
## 
## tau^2 (estimated amount of residual heterogeneity):     0.0117 (SE = 0.0079)
## tau (square root of estimated tau^2 value):             0.1081
## I^2 (residual heterogeneity / unaccounted variability): 97.45%
## H^2 (unaccounted variability / sampling variability):   39.19
## R^2 (amount of heterogeneity accounted for):            0.00%
## 
## Test for Residual Heterogeneity:
## QE(df = 5) = 174.5812, p-val < .0001
## 
## Test of Moderators (coefficients 2:4):
## QM(df = 3) = 2.2317, p-val = 0.5257
## 
## Model Results:
## 
##                         estimate      se     zval    pval    ci.lb   ci.ub 
## intrcpt                  -0.4482  0.3175  -1.4115  0.1581  -1.0705  0.1741    
## continentEurope           0.0728  0.1038   0.7014  0.4830  -0.1306  0.2762    
## continentNorth America    0.1225  0.1194   1.0256  0.3051  -0.1116  0.3565    
## mean.age                  0.0023  0.0067   0.3454  0.7298  -0.0108  0.0155    
## 
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

Note: Scale range was not included as a moderator in the meta-analysis results because all samples used the same measure scale of general risk-taking propensity

Linear with gender interaction model

Meta analysis:
Age effect results

## 
## Random-Effects Model (k = 9; tau^2 estimator: REML)
## 
##   logLik  deviance       AIC       BIC      AICc 
##  13.5147  -27.0293  -23.0293  -22.8704  -20.6293   
## 
## tau^2 (estimated amount of total heterogeneity): 0.0015 (SE = 0.0008)
## tau (square root of estimated tau^2 value):      0.0392
## I^2 (total heterogeneity / total variability):   96.71%
## H^2 (total variability / sampling variability):  30.36
## 
## Test for Heterogeneity:
## Q(df = 8) = 130.5119, p-val < .0001
## 
## Model Results:
## 
## estimate      se     zval    pval    ci.lb    ci.ub 
##  -0.0760  0.0136  -5.5711  <.0001  -0.1027  -0.0493  *** 
## 
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

Gender effect results

## 
## Random-Effects Model (k = 9; tau^2 estimator: REML)
## 
##   logLik  deviance       AIC       BIC      AICc 
##   6.5649  -13.1298   -9.1298   -8.9709   -6.7298   
## 
## tau^2 (estimated amount of total heterogeneity): 0.0109 (SE = 0.0058)
## tau (square root of estimated tau^2 value):      0.1042
## I^2 (total heterogeneity / total variability):   97.51%
## H^2 (total variability / sampling variability):  40.21
## 
## Test for Heterogeneity:
## Q(df = 8) = 277.5798, p-val < .0001
## 
## Model Results:
## 
## estimate      se     zval    pval    ci.lb    ci.ub 
##  -0.2485  0.0359  -6.9308  <.0001  -0.3188  -0.1783  *** 
## 
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

Age $\times$ Gender effect results

## 
## Random-Effects Model (k = 9; tau^2 estimator: REML)
## 
##   logLik  deviance       AIC       BIC      AICc 
##  18.2503  -36.5006  -32.5006  -32.3417  -30.1006   
## 
## tau^2 (estimated amount of total heterogeneity): 0.0004 (SE = 0.0003)
## tau (square root of estimated tau^2 value):      0.0200
## I^2 (total heterogeneity / total variability):   80.53%
## H^2 (total variability / sampling variability):  5.14
## 
## Test for Heterogeneity:
## Q(df = 8) = 36.2545, p-val < .0001
## 
## Model Results:
## 
## estimate      se    zval    pval    ci.lb   ci.ub 
##   0.0006  0.0079  0.0746  0.9405  -0.0150  0.0162    
## 
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

Meta analysis with three moderators (continent, mean age, scale range):
Age effect results

## 
## Mixed-Effects Model (k = 9; tau^2 estimator: REML)
## 
##   logLik  deviance       AIC       BIC      AICc 
##   8.2398  -16.4796   -6.4796   -8.4324   53.5204   
## 
## tau^2 (estimated amount of residual heterogeneity):     0.0017 (SE = 0.0012)
## tau (square root of estimated tau^2 value):             0.0412
## I^2 (residual heterogeneity / unaccounted variability): 95.98%
## H^2 (unaccounted variability / sampling variability):   24.86
## R^2 (amount of heterogeneity accounted for):            0.00%
## 
## Test for Residual Heterogeneity:
## QE(df = 5) = 66.8980, p-val < .0001
## 
## Test of Moderators (coefficients 2:4):
## QM(df = 3) = 2.9170, p-val = 0.4046
## 
## Model Results:
## 
##                         estimate      se     zval    pval    ci.lb   ci.ub 
## intrcpt                  -0.1098  0.1225  -0.8962  0.3701  -0.3498  0.1303    
## continentEurope          -0.0071  0.0401  -0.1768  0.8597  -0.0857  0.0715    
## continentNorth America    0.0440  0.0460   0.9556  0.3393  -0.0462  0.1342    
## mean.age                  0.0004  0.0026   0.1592  0.8735  -0.0047  0.0055    
## 
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

Gender effect results

## 
## Mixed-Effects Model (k = 9; tau^2 estimator: REML)
## 
##   logLik  deviance       AIC       BIC      AICc 
##   3.7981   -7.5961    2.4039    0.4511   62.4039   
## 
## tau^2 (estimated amount of residual heterogeneity):     0.0123 (SE = 0.0083)
## tau (square root of estimated tau^2 value):             0.1110
## I^2 (residual heterogeneity / unaccounted variability): 97.36%
## H^2 (unaccounted variability / sampling variability):   37.87
## R^2 (amount of heterogeneity accounted for):            0.00%
## 
## Test for Residual Heterogeneity:
## QE(df = 5) = 169.2044, p-val < .0001
## 
## Test of Moderators (coefficients 2:4):
## QM(df = 3) = 2.0721, p-val = 0.5576
## 
## Model Results:
## 
##                         estimate      se     zval    pval    ci.lb   ci.ub 
## intrcpt                  -0.4702  0.3284  -1.4321  0.1521  -1.1138  0.1733    
## continentEurope           0.0538  0.1066   0.5042  0.6141  -0.1552  0.2627    
## continentNorth America    0.1097  0.1226   0.8945  0.3711  -0.1306  0.3499    
## mean.age                  0.0031  0.0069   0.4489  0.6535  -0.0105  0.0167    
## 
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

Age $\times$ Gender effect results

## 
## Mixed-Effects Model (k = 9; tau^2 estimator: REML)
## 
##   logLik  deviance       AIC       BIC      AICc 
##  11.4690  -22.9380  -12.9380  -14.8908   47.0620   
## 
## tau^2 (estimated amount of residual heterogeneity):     0.0003 (SE = 0.0003)
## tau (square root of estimated tau^2 value):             0.0166
## I^2 (residual heterogeneity / unaccounted variability): 67.34%
## H^2 (unaccounted variability / sampling variability):   3.06
## R^2 (amount of heterogeneity accounted for):            31.31%
## 
## Test for Residual Heterogeneity:
## QE(df = 5) = 14.3012, p-val = 0.0138
## 
## Test of Moderators (coefficients 2:4):
## QM(df = 3) = 4.5797, p-val = 0.2053
## 
## Model Results:
## 
##                         estimate      se     zval    pval    ci.lb   ci.ub 
## intrcpt                   0.0893  0.0577   1.5475  0.1217  -0.0238  0.2023    
## continentEurope          -0.0212  0.0195  -1.0834  0.2786  -0.0595  0.0171    
## continentNorth America   -0.0104  0.0225  -0.4612  0.6447  -0.0544  0.0337    
## mean.age                 -0.0015  0.0012  -1.1980  0.2309  -0.0039  0.0009    
## 
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

Note: Scale range was not included as a moderator in the meta-analysis results because all samples used the same measure scale of general risk-taking propensity

Quadratic model

Meta analysis:
Age effect results

## 
## Random-Effects Model (k = 7; tau^2 estimator: REML)
## 
##   logLik  deviance       AIC       BIC      AICc 
##  11.1997  -22.3994  -18.3994  -18.8159  -14.3994   
## 
## tau^2 (estimated amount of total heterogeneity): 0.0013 (SE = 0.0008)
## tau (square root of estimated tau^2 value):      0.0361
## I^2 (total heterogeneity / total variability):   98.05%
## H^2 (total variability / sampling variability):  51.34
## 
## Test for Heterogeneity:
## Q(df = 6) = 203.3039, p-val < .0001
## 
## Model Results:
## 
## estimate      se     zval    pval    ci.lb    ci.ub 
##  -0.0709  0.0141  -5.0430  <.0001  -0.0985  -0.0433  *** 
## 
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

Age${ }^{2}$ effect

## 
## Random-Effects Model (k = 7; tau^2 estimator: REML)
## 
##   logLik  deviance       AIC       BIC      AICc 
##  18.0617  -36.1234  -32.1234  -32.5399  -28.1234   
## 
## tau^2 (estimated amount of total heterogeneity): 0.0001 (SE = 0.0001)
## tau (square root of estimated tau^2 value):      0.0115
## I^2 (total heterogeneity / total variability):   94.87%
## H^2 (total variability / sampling variability):  19.49
## 
## Test for Heterogeneity:
## Q(df = 6) = 188.9191, p-val < .0001
## 
## Model Results:
## 
## estimate      se     zval    pval    ci.lb   ci.ub 
##  -0.0029  0.0046  -0.6398  0.5223  -0.0119  0.0061    
## 
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

Meta analysis with three moderators (continent, mean age, scale range):
Age effect results

## 
## Mixed-Effects Model (k = 7; tau^2 estimator: REML)
## 
##   logLik  deviance       AIC       BIC      AICc 
##   7.4469  -14.8939   -4.8939   -9.4008   55.1061   
## 
## tau^2 (estimated amount of residual heterogeneity):     0.0004 (SE = 0.0003)
## tau (square root of estimated tau^2 value):             0.0194
## I^2 (residual heterogeneity / unaccounted variability): 90.81%
## H^2 (unaccounted variability / sampling variability):   10.88
## R^2 (amount of heterogeneity accounted for):            71.05%
## 
## Test for Residual Heterogeneity:
## QE(df = 3) = 40.3182, p-val < .0001
## 
## Test of Moderators (coefficients 2:4):
## QM(df = 3) = 15.5459, p-val = 0.0014
## 
## Model Results:
## 
##                         estimate      se     zval    pval    ci.lb   ci.ub 
## intrcpt                  -0.0978  0.0723  -1.3529  0.1761  -0.2394  0.0439    
## continentEurope          -0.0205  0.0215  -0.9537  0.3402  -0.0625  0.0216    
## continentNorth America    0.0507  0.0226   2.2428  0.0249   0.0064  0.0949  * 
## mean.age                  0.0002  0.0015   0.1567  0.8755  -0.0028  0.0033    
## 
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

Age${ }^{2}$ effect

## 
## Mixed-Effects Model (k = 7; tau^2 estimator: REML)
## 
##   logLik  deviance       AIC       BIC      AICc 
##   8.1458  -16.2915   -6.2915  -10.7985   53.7085   
## 
## tau^2 (estimated amount of residual heterogeneity):     0.0002 (SE = 0.0002)
## tau (square root of estimated tau^2 value):             0.0156
## I^2 (residual heterogeneity / unaccounted variability): 95.14%
## H^2 (unaccounted variability / sampling variability):   20.56
## R^2 (amount of heterogeneity accounted for):            0.00%
## 
## Test for Residual Heterogeneity:
## QE(df = 3) = 56.5705, p-val < .0001
## 
## Test of Moderators (coefficients 2:4):
## QM(df = 3) = 0.2592, p-val = 0.9675
## 
## Model Results:
## 
##                         estimate      se     zval    pval    ci.lb   ci.ub 
## intrcpt                  -0.0001  0.0482  -0.0022  0.9983  -0.0946  0.0944    
## continentEurope           0.0069  0.0167   0.4130  0.6796  -0.0258  0.0396    
## continentNorth America    0.0083  0.0177   0.4685  0.6394  -0.0263  0.0429    
## mean.age                 -0.0002  0.0010  -0.1603  0.8726  -0.0022  0.0018    
## 
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

Note: Scale range was not included as a moderator in the meta-analysis results because all samples used the same measure scale of general risk-taking propensity

Quadratic with gender model

Meta analysis:
Age effect results

## 
## Random-Effects Model (k = 7; tau^2 estimator: REML)
## 
##   logLik  deviance       AIC       BIC      AICc 
##  11.5455  -23.0911  -19.0911  -19.5075  -15.0911   
## 
## tau^2 (estimated amount of total heterogeneity): 0.0012 (SE = 0.0007)
## tau (square root of estimated tau^2 value):      0.0340
## I^2 (total heterogeneity / total variability):   97.86%
## H^2 (total variability / sampling variability):  46.75
## 
## Test for Heterogeneity:
## Q(df = 6) = 179.0352, p-val < .0001
## 
## Model Results:
## 
## estimate      se     zval    pval    ci.lb    ci.ub 
##  -0.0732  0.0133  -5.5229  <.0001  -0.0992  -0.0472  *** 
## 
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

Age${ }^{2}$ effect

## 
## Random-Effects Model (k = 7; tau^2 estimator: REML)
## 
##   logLik  deviance       AIC       BIC      AICc 
##  18.7525  -37.5050  -33.5050  -33.9215  -29.5050   
## 
## tau^2 (estimated amount of total heterogeneity): 0.0001 (SE = 0.0001)
## tau (square root of estimated tau^2 value):      0.0102
## I^2 (total heterogeneity / total variability):   93.74%
## H^2 (total variability / sampling variability):  15.98
## 
## Test for Heterogeneity:
## Q(df = 6) = 167.3905, p-val < .0001
## 
## Model Results:
## 
## estimate      se     zval    pval    ci.lb   ci.ub 
##  -0.0019  0.0041  -0.4559  0.6485  -0.0099  0.0062    
## 
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

Gender effect results

## 
## Random-Effects Model (k = 7; tau^2 estimator: REML)
## 
##   logLik  deviance       AIC       BIC      AICc 
##   6.5505  -13.1010   -9.1010   -9.5174   -5.1010   
## 
## tau^2 (estimated amount of total heterogeneity): 0.0063 (SE = 0.0038)
## tau (square root of estimated tau^2 value):      0.0794
## I^2 (total heterogeneity / total variability):   97.19%
## H^2 (total variability / sampling variability):  35.57
## 
## Test for Heterogeneity:
## Q(df = 6) = 180.0552, p-val < .0001
## 
## Model Results:
## 
## estimate      se     zval    pval    ci.lb    ci.ub 
##  -0.2793  0.0306  -9.1233  <.0001  -0.3393  -0.2193  *** 
## 
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

Meta analysis with three moderators (continent, mean age, scale range):
Age effect results

## 
## Mixed-Effects Model (k = 7; tau^2 estimator: REML)
## 
##   logLik  deviance       AIC       BIC      AICc 
##   7.8304  -15.6608   -5.6608  -10.1677   54.3392   
## 
## tau^2 (estimated amount of residual heterogeneity):     0.0003 (SE = 0.0003)
## tau (square root of estimated tau^2 value):             0.0169
## I^2 (residual heterogeneity / unaccounted variability): 88.42%
## H^2 (unaccounted variability / sampling variability):   8.64
## R^2 (amount of heterogeneity accounted for):            75.24%
## 
## Test for Residual Heterogeneity:
## QE(df = 3) = 32.1882, p-val < .0001
## 
## Test of Moderators (coefficients 2:4):
## QM(df = 3) = 17.9469, p-val = 0.0005
## 
## Model Results:
## 
##                         estimate      se     zval    pval    ci.lb   ci.ub 
## intrcpt                  -0.0858  0.0658  -1.3029  0.1926  -0.2148  0.0433    
## continentEurope          -0.0170  0.0190  -0.8945  0.3710  -0.0541  0.0202    
## continentNorth America    0.0513  0.0199   2.5721  0.0101   0.0122  0.0904  * 
## mean.age                 -0.0001  0.0014  -0.0454  0.9638  -0.0028  0.0027    
## 
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

Age${ }^{2}$ effect

## 
## Mixed-Effects Model (k = 7; tau^2 estimator: REML)
## 
##   logLik  deviance       AIC       BIC      AICc 
##   8.6000  -17.2001   -7.2001  -11.7070   52.7999   
## 
## tau^2 (estimated amount of residual heterogeneity):     0.0002 (SE = 0.0002)
## tau (square root of estimated tau^2 value):             0.0132
## I^2 (residual heterogeneity / unaccounted variability): 93.54%
## H^2 (unaccounted variability / sampling variability):   15.47
## R^2 (amount of heterogeneity accounted for):            0.00%
## 
## Test for Residual Heterogeneity:
## QE(df = 3) = 42.0114, p-val < .0001
## 
## Test of Moderators (coefficients 2:4):
## QM(df = 3) = 0.4738, p-val = 0.9246
## 
## Model Results:
## 
##                         estimate      se     zval    pval    ci.lb   ci.ub 
## intrcpt                  -0.0039  0.0415  -0.0947  0.9246  -0.0853  0.0775    
## continentEurope           0.0091  0.0143   0.6375  0.5238  -0.0189  0.0372    
## continentNorth America    0.0077  0.0152   0.5063  0.6127  -0.0221  0.0374    
## mean.age                 -0.0001  0.0009  -0.0862  0.9313  -0.0018  0.0017    
## 
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

Gender effect results

## 
## Mixed-Effects Model (k = 7; tau^2 estimator: REML)
## 
##   logLik  deviance       AIC       BIC      AICc 
##   5.8282  -11.6564   -1.6564   -6.1633   58.3436   
## 
## tau^2 (estimated amount of residual heterogeneity):     0.0009 (SE = 0.0009)
## tau (square root of estimated tau^2 value):             0.0293
## I^2 (residual heterogeneity / unaccounted variability): 77.93%
## H^2 (unaccounted variability / sampling variability):   4.53
## R^2 (amount of heterogeneity accounted for):            86.42%
## 
## Test for Residual Heterogeneity:
## QE(df = 3) = 11.4389, p-val = 0.0096
## 
## Test of Moderators (coefficients 2:4):
## QM(df = 3) = 31.8846, p-val < .0001
## 
## Model Results:
## 
##                         estimate      se     zval    pval    ci.lb    ci.ub 
## intrcpt                  -0.2912  0.0975  -2.9879  0.0028  -0.4822  -0.1002 
## continentEurope           0.0047  0.0342   0.1365  0.8914  -0.0623   0.0716 
## continentNorth America    0.1540  0.0380   4.0516  <.0001   0.0795   0.2285 
## mean.age                 -0.0011  0.0021  -0.5120  0.6086  -0.0051   0.0030 
##  
## intrcpt                  ** 
## continentEurope 
## continentNorth America  *** 
## mean.age 
## 
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

5.2. Financial risk-taking

Intercept only model

Meta analysis:
ICC’s results

## 
## Random-Effects Model (k = 20; tau^2 estimator: REML)
## 
##   logLik  deviance       AIC       BIC      AICc 
##  14.2882  -28.5763  -24.5763  -22.6875  -23.8263   
## 
## tau^2 (estimated amount of total heterogeneity): 0.0124 (SE = 0.0042)
## tau (square root of estimated tau^2 value):      0.1112
## I^2 (total heterogeneity / total variability):   99.39%
## H^2 (total variability / sampling variability):  163.87
## 
## Test for Heterogeneity:
## Q(df = 19) = 2105.3159, p-val < .0001
## 
## Model Results:
## 
## estimate      se     zval    pval   ci.lb   ci.ub 
##   0.3624  0.0255  14.2287  <.0001  0.3124  0.4123  *** 
## 
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

Meta analysis with three moderators (continent, mean age, scale range):
ICC’s results

## 
## Mixed-Effects Model (k = 20; tau^2 estimator: REML)
## 
##   logLik  deviance       AIC       BIC      AICc 
##  13.8373  -27.6746  -13.6746   -9.2012    4.9921   
## 
## tau^2 (estimated amount of residual heterogeneity):     0.0075 (SE = 0.0031)
## tau (square root of estimated tau^2 value):             0.0869
## I^2 (residual heterogeneity / unaccounted variability): 96.37%
## H^2 (unaccounted variability / sampling variability):   27.55
## R^2 (amount of heterogeneity accounted for):            38.96%
## 
## Test for Residual Heterogeneity:
## QE(df = 14) = 783.4939, p-val < .0001
## 
## Test of Moderators (coefficients 2:6):
## QM(df = 5) = 16.4398, p-val = 0.0057
## 
## Model Results:
## 
##                         estimate      se     zval    pval    ci.lb    ci.ub 
## intrcpt                   2.0383  0.6677   3.0528  0.0023   0.7297   3.3469  ** 
## continentEurope          -0.0144  0.1054  -0.1370  0.8910  -0.2210   0.1921     
## continentNorth America    0.4751  0.2161   2.1989  0.0279   0.0516   0.8986   * 
## continentOceania         -0.2078  0.2016  -1.0312  0.3025  -0.6029   0.1872     
## mean.age                 -0.0239  0.0084  -2.8357  0.0046  -0.0404  -0.0074  ** 
## scale                    -0.0366  0.0239  -1.5324  0.1254  -0.0833   0.0102     
## 
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

Fixed effect model

Meta analysis:
Age effect results

## 
## Random-Effects Model (k = 20; tau^2 estimator: REML)
## 
##   logLik  deviance       AIC       BIC      AICc 
##  32.0436  -64.0872  -60.0872  -58.1983  -59.3372   
## 
## tau^2 (estimated amount of total heterogeneity): 0.0017 (SE = 0.0006)
## tau (square root of estimated tau^2 value):      0.0411
## I^2 (total heterogeneity / total variability):   96.53%
## H^2 (total variability / sampling variability):  28.82
## 
## Test for Heterogeneity:
## Q(df = 19) = 338.8796, p-val < .0001
## 
## Model Results:
## 
## estimate      se      zval    pval    ci.lb    ci.ub 
##  -0.1131  0.0098  -11.4875  <.0001  -0.1324  -0.0938  *** 
## 
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

Meta analysis with three moderators (continent, mean age, scale range):
Age effect results

## 
## Mixed-Effects Model (k = 20; tau^2 estimator: REML)
## 
##   logLik  deviance       AIC       BIC      AICc 
##  23.8919  -47.7839  -33.7839  -29.3105  -15.1172   
## 
## tau^2 (estimated amount of residual heterogeneity):     0.0015 (SE = 0.0007)
## tau (square root of estimated tau^2 value):             0.0388
## I^2 (residual heterogeneity / unaccounted variability): 91.04%
## H^2 (unaccounted variability / sampling variability):   11.16
## R^2 (amount of heterogeneity accounted for):            10.89%
## 
## Test for Residual Heterogeneity:
## QE(df = 14) = 90.9219, p-val < .0001
## 
## Test of Moderators (coefficients 2:6):
## QM(df = 5) = 6.3944, p-val = 0.2697
## 
## Model Results:
## 
##                         estimate      se     zval    pval    ci.lb   ci.ub 
## intrcpt                   0.1629  0.3044   0.5350  0.5926  -0.4338  0.7595    
## continentEurope          -0.0086  0.0535  -0.1612  0.8719  -0.1136  0.0963    
## continentNorth America    0.0278  0.1009   0.2750  0.7833  -0.1701  0.2256    
## continentOceania         -0.0024  0.0944  -0.0250  0.9801  -0.1874  0.1827    
## mean.age                 -0.0042  0.0038  -1.0995  0.2716  -0.0117  0.0033    
## scale                    -0.0015  0.0108  -0.1419  0.8871  -0.0227  0.0196    
## 
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

Linear model

Meta analysis:
Age effect results

## 
## Random-Effects Model (k = 20; tau^2 estimator: REML)
## 
##   logLik  deviance       AIC       BIC      AICc 
##  31.7788  -63.5577  -59.5577  -57.6688  -58.8077   
## 
## tau^2 (estimated amount of total heterogeneity): 0.0018 (SE = 0.0006)
## tau (square root of estimated tau^2 value):      0.0420
## I^2 (total heterogeneity / total variability):   96.32%
## H^2 (total variability / sampling variability):  27.17
## 
## Test for Heterogeneity:
## Q(df = 19) = 317.6674, p-val < .0001
## 
## Model Results:
## 
## estimate      se      zval    pval    ci.lb    ci.ub 
##  -0.1133  0.0100  -11.3021  <.0001  -0.1329  -0.0936  *** 
## 
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

Meta analysis with three moderators (continent, mean age, scale range):
Age effect results

## 
## Mixed-Effects Model (k = 20; tau^2 estimator: REML)
## 
##   logLik  deviance       AIC       BIC      AICc 
##  23.3257  -46.6513  -32.6513  -28.1779  -13.9847   
## 
## tau^2 (estimated amount of residual heterogeneity):     0.0017 (SE = 0.0007)
## tau (square root of estimated tau^2 value):             0.0415
## I^2 (residual heterogeneity / unaccounted variability): 92.14%
## H^2 (unaccounted variability / sampling variability):   12.73
## R^2 (amount of heterogeneity accounted for):            2.52%
## 
## Test for Residual Heterogeneity:
## QE(df = 14) = 113.9503, p-val < .0001
## 
## Test of Moderators (coefficients 2:6):
## QM(df = 5) = 5.1231, p-val = 0.4010
## 
## Model Results:
## 
##                         estimate      se     zval    pval    ci.lb   ci.ub 
## intrcpt                   0.1047  0.3243   0.3230  0.7467  -0.5308  0.7403    
## continentEurope          -0.0015  0.0553  -0.0276  0.9780  -0.1099  0.1068    
## continentNorth America    0.0207  0.1067   0.1938  0.8463  -0.1885  0.2299    
## continentOceania          0.0132  0.0997   0.1328  0.8943  -0.1822  0.2087    
## mean.age                 -0.0035  0.0041  -0.8584  0.3907  -0.0115  0.0045    
## scale                    -0.0001  0.0115  -0.0043  0.9965  -0.0226  0.0225    
## 
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

Linear with gender model

Meta analysis:
Age effect results

## 
## Random-Effects Model (k = 20; tau^2 estimator: REML)
## 
##   logLik  deviance       AIC       BIC      AICc 
##  32.6391  -65.2782  -61.2782  -59.3893  -60.5282   
## 
## tau^2 (estimated amount of total heterogeneity): 0.0016 (SE = 0.0006)
## tau (square root of estimated tau^2 value):      0.0400
## I^2 (total heterogeneity / total variability):   96.06%
## H^2 (total variability / sampling variability):  25.40
## 
## Test for Heterogeneity:
## Q(df = 19) = 304.1420, p-val < .0001
## 
## Model Results:
## 
## estimate      se      zval    pval    ci.lb    ci.ub 
##  -0.1141  0.0096  -11.9133  <.0001  -0.1329  -0.0954  *** 
## 
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

Gender effect results

## 
## Random-Effects Model (k = 20; tau^2 estimator: REML)
## 
##   logLik  deviance       AIC       BIC      AICc 
##  14.8113  -29.6226  -25.6226  -23.7338  -24.8726   
## 
## tau^2 (estimated amount of total heterogeneity): 0.0113 (SE = 0.0040)
## tau (square root of estimated tau^2 value):      0.1064
## I^2 (total heterogeneity / total variability):   95.93%
## H^2 (total variability / sampling variability):  24.57
## 
## Test for Heterogeneity:
## Q(df = 19) = 706.9394, p-val < .0001
## 
## Model Results:
## 
## estimate      se      zval    pval    ci.lb    ci.ub 
##  -0.2752  0.0248  -11.0890  <.0001  -0.3239  -0.2266  *** 
## 
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

Meta analysis with three moderators (continent, mean age, scale range):
Age effect results

## 
## Mixed-Effects Model (k = 20; tau^2 estimator: REML)
## 
##   logLik  deviance       AIC       BIC      AICc 
##  24.0730  -48.1460  -34.1460  -29.6726  -15.4793   
## 
## tau^2 (estimated amount of residual heterogeneity):     0.0015 (SE = 0.0007)
## tau (square root of estimated tau^2 value):             0.0394
## I^2 (residual heterogeneity / unaccounted variability): 91.53%
## H^2 (unaccounted variability / sampling variability):   11.81
## R^2 (amount of heterogeneity accounted for):            3.38%
## 
## Test for Residual Heterogeneity:
## QE(df = 14) = 115.1181, p-val < .0001
## 
## Test of Moderators (coefficients 2:6):
## QM(df = 5) = 5.3920, p-val = 0.3699
## 
## Model Results:
## 
##                         estimate      se     zval    pval    ci.lb   ci.ub 
## intrcpt                   0.1238  0.3085   0.4015  0.6881  -0.4808  0.7284    
## continentEurope           0.0028  0.0531   0.0530  0.9577  -0.1013  0.1069    
## continentNorth America    0.0324  0.1017   0.3188  0.7499  -0.1669  0.2318    
## continentOceania          0.0122  0.0951   0.1283  0.8979  -0.1742  0.1986    
## mean.age                 -0.0038  0.0039  -0.9721  0.3310  -0.0114  0.0038    
## scale                    -0.0015  0.0110  -0.1389  0.8895  -0.0230  0.0199    
## 
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

Gender effect results

## 
## Mixed-Effects Model (k = 20; tau^2 estimator: REML)
## 
##   logLik  deviance       AIC       BIC      AICc 
##  12.5698  -25.1396  -11.1396   -6.6662    7.5271   
## 
## tau^2 (estimated amount of residual heterogeneity):     0.0079 (SE = 0.0034)
## tau (square root of estimated tau^2 value):             0.0889
## I^2 (residual heterogeneity / unaccounted variability): 91.85%
## H^2 (unaccounted variability / sampling variability):   12.27
## R^2 (amount of heterogeneity accounted for):            30.07%
## 
## Test for Residual Heterogeneity:
## QE(df = 14) = 149.8105, p-val < .0001
## 
## Test of Moderators (coefficients 2:6):
## QM(df = 5) = 11.1645, p-val = 0.0482
## 
## Model Results:
## 
##                         estimate      se     zval    pval    ci.lb   ci.ub 
## intrcpt                  -1.2867  0.7077  -1.8180  0.0691  -2.6738  0.1004  . 
## continentEurope           0.0737  0.1110   0.6639  0.5067  -0.1439  0.2913    
## continentNorth America   -0.1804  0.2277  -0.7923  0.4282  -0.6266  0.2658    
## continentOceania          0.4294  0.2124   2.0222  0.0432   0.0132  0.8456  * 
## mean.age                  0.0141  0.0089   1.5785  0.1144  -0.0034  0.0316    
## scale                     0.0110  0.0252   0.4375  0.6617  -0.0384  0.0604    
## 
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

Linear with gender interaction model

Meta analysis:
Age effect results

## 
## Random-Effects Model (k = 20; tau^2 estimator: REML)
## 
##   logLik  deviance       AIC       BIC      AICc 
##  27.3527  -54.7053  -50.7053  -48.8165  -49.9553   
## 
## tau^2 (estimated amount of total heterogeneity): 0.0027 (SE = 0.0010)
## tau (square root of estimated tau^2 value):      0.0517
## I^2 (total heterogeneity / total variability):   95.09%
## H^2 (total variability / sampling variability):  20.37
## 
## Test for Heterogeneity:
## Q(df = 19) = 245.0094, p-val < .0001
## 
## Model Results:
## 
## estimate      se      zval    pval    ci.lb    ci.ub 
##  -0.1321  0.0126  -10.4923  <.0001  -0.1568  -0.1074  *** 
## 
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

Gender effect results

## 
## Random-Effects Model (k = 20; tau^2 estimator: REML)
## 
##   logLik  deviance       AIC       BIC      AICc 
##  10.4825  -20.9650  -16.9650  -15.0761  -16.2150   
## 
## tau^2 (estimated amount of total heterogeneity): 0.0147 (SE = 0.0058)
## tau (square root of estimated tau^2 value):      0.1213
## I^2 (total heterogeneity / total variability):   94.11%
## H^2 (total variability / sampling variability):  16.97
## 
## Test for Heterogeneity:
## Q(df = 19) = 510.6203, p-val < .0001
## 
## Model Results:
## 
## estimate      se      zval    pval    ci.lb    ci.ub 
##  -0.3215  0.0302  -10.6564  <.0001  -0.3807  -0.2624  *** 
## 
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

Age $\times$ Gender effect results

## 
## Random-Effects Model (k = 20; tau^2 estimator: REML)
## 
##   logLik  deviance       AIC       BIC      AICc 
##  32.8216  -65.6433  -61.6433  -59.7544  -60.8933   
## 
## tau^2 (estimated amount of total heterogeneity): 0.0009 (SE = 0.0005)
## tau (square root of estimated tau^2 value):      0.0307
## I^2 (total heterogeneity / total variability):   77.94%
## H^2 (total variability / sampling variability):  4.53
## 
## Test for Heterogeneity:
## Q(df = 19) = 69.6500, p-val < .0001
## 
## Model Results:
## 
## estimate      se    zval    pval   ci.lb   ci.ub 
##   0.0301  0.0090  3.3378  0.0008  0.0124  0.0477  *** 
## 
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

Meta analysis with three moderators (continent, mean age, scale range):
Age effect results

## 
## Mixed-Effects Model (k = 20; tau^2 estimator: REML)
## 
##   logLik  deviance       AIC       BIC      AICc 
##  20.3158  -40.6316  -26.6316  -22.1582   -7.9649   
## 
## tau^2 (estimated amount of residual heterogeneity):     0.0025 (SE = 0.0011)
## tau (square root of estimated tau^2 value):             0.0501
## I^2 (residual heterogeneity / unaccounted variability): 88.94%
## H^2 (unaccounted variability / sampling variability):   9.05
## R^2 (amount of heterogeneity accounted for):            5.79%
## 
## Test for Residual Heterogeneity:
## QE(df = 14) = 76.9467, p-val < .0001
## 
## Test of Moderators (coefficients 2:6):
## QM(df = 5) = 5.8616, p-val = 0.3199
## 
## Model Results:
## 
##                         estimate      se     zval    pval    ci.lb   ci.ub 
## intrcpt                   0.1468  0.3972   0.3697  0.7116  -0.6317  0.9253    
## continentEurope           0.0072  0.0714   0.1009  0.9196  -0.1328  0.1472    
## continentNorth America    0.0936  0.1324   0.7068  0.4797  -0.1659  0.3530    
## continentOceania          0.0306  0.1238   0.2468  0.8051  -0.2121  0.2733    
## mean.age                 -0.0045  0.0050  -0.9068  0.3645  -0.0143  0.0053    
## scale                    -0.0020  0.0140  -0.1439  0.8855  -0.0295  0.0255    
## 
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

Gender effect results

## 
## Mixed-Effects Model (k = 20; tau^2 estimator: REML)
## 
##   logLik  deviance       AIC       BIC      AICc 
##   7.2902  -14.5804   -0.5804    3.8930   18.0862   
## 
## tau^2 (estimated amount of residual heterogeneity):     0.0145 (SE = 0.0068)
## tau (square root of estimated tau^2 value):             0.1206
## I^2 (residual heterogeneity / unaccounted variability): 87.43%
## H^2 (unaccounted variability / sampling variability):   7.96
## R^2 (amount of heterogeneity accounted for):            1.12%
## 
## Test for Residual Heterogeneity:
## QE(df = 14) = 79.4096, p-val < .0001
## 
## Test of Moderators (coefficients 2:6):
## QM(df = 5) = 4.4740, p-val = 0.4834
## 
## Model Results:
## 
##                         estimate      se     zval    pval    ci.lb   ci.ub 
## intrcpt                  -0.9368  0.9721  -0.9637  0.3352  -2.8421  0.9684    
## continentEurope           0.0979  0.1897   0.5161  0.6058  -0.2739  0.4696    
## continentNorth America    0.0526  0.3310   0.1589  0.8738  -0.5961  0.7013    
## continentOceania          0.4244  0.3107   1.3663  0.1718  -0.1844  1.0333    
## mean.age                  0.0076  0.0122   0.6190  0.5359  -0.0164  0.0315    
## scale                     0.0067  0.0342   0.1965  0.8442  -0.0603  0.0737    
## 
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

Age $\times$ Gender effect results

## 
## Mixed-Effects Model (k = 20; tau^2 estimator: REML)
## 
## tau^2 (estimated amount of residual heterogeneity):     0.0008 (SE = 0.0006)
## tau (square root of estimated tau^2 value):             0.0275
## I^2 (residual heterogeneity / unaccounted variability): 56.45%
## H^2 (unaccounted variability / sampling variability):   2.30
## R^2 (amount of heterogeneity accounted for):            19.57%
## 
## Test for Residual Heterogeneity:
## QE(df = 14) = 30.3307, p-val = 0.0069
## 
## Test of Moderators (coefficients 2:6):
## QM(df = 5) = 7.0193, p-val = 0.2192
## 
## Model Results:
## 
##                         estimate      se     zval    pval    ci.lb   ci.ub 
## intrcpt                   0.0611  0.2589   0.2361  0.8133  -0.4463  0.5685    
## continentEurope          -0.0169  0.0690  -0.2455  0.8061  -0.1521  0.1182    
## continentNorth America   -0.0904  0.0977  -0.9253  0.3548  -0.2820  0.1011    
## continentOceania         -0.0595  0.0931  -0.6393  0.5226  -0.2421  0.1230    
## mean.age                  0.0000  0.0032   0.0045  0.9964  -0.0063  0.0063    
## scale                    -0.0014  0.0087  -0.1589  0.8737  -0.0184  0.0156    
## 
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

Quadratic model

Meta analysis:
Age effect results

## 
## Random-Effects Model (k = 16; tau^2 estimator: REML)
## 
##   logLik  deviance       AIC       BIC      AICc 
##  15.3540  -30.7079  -26.7079  -25.2918  -25.7079   
## 
## tau^2 (estimated amount of total heterogeneity): 0.0040 (SE = 0.0022)
## tau (square root of estimated tau^2 value):      0.0632
## I^2 (total heterogeneity / total variability):   96.10%
## H^2 (total variability / sampling variability):  25.64
## 
## Test for Heterogeneity:
## Q(df = 15) = 79.9806, p-val < .0001
## 
## Model Results:
## 
## estimate      se     zval    pval    ci.lb    ci.ub 
##  -0.1138  0.0198  -5.7362  <.0001  -0.1527  -0.0749  *** 
## 
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

Age${ }^{2}$ effect

## 
## Random-Effects Model (k = 16; tau^2 estimator: REML)
## 
##   logLik  deviance       AIC       BIC      AICc 
##  37.1833  -74.3665  -70.3665  -68.9504  -69.3665   
## 
## tau^2 (estimated amount of total heterogeneity): 0.0003 (SE = 0.0001)
## tau (square root of estimated tau^2 value):      0.0163
## I^2 (total heterogeneity / total variability):   89.50%
## H^2 (total variability / sampling variability):  9.52
## 
## Test for Heterogeneity:
## Q(df = 15) = 306.3181, p-val < .0001
## 
## Model Results:
## 
## estimate      se    zval    pval    ci.lb   ci.ub 
##   0.0017  0.0052  0.3379  0.7354  -0.0084  0.0119    
## 
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

Meta analysis with three moderators (continent, mean age, scale range):
Age effect results

## 
## Mixed-Effects Model (k = 16; tau^2 estimator: REML)
## 
##   logLik  deviance       AIC       BIC      AICc 
##  10.1804  -20.3608   -8.3608   -5.9734   12.6392   
## 
## tau^2 (estimated amount of residual heterogeneity):     0.0050 (SE = 0.0033)
## tau (square root of estimated tau^2 value):             0.0709
## I^2 (residual heterogeneity / unaccounted variability): 92.44%
## H^2 (unaccounted variability / sampling variability):   13.23
## R^2 (amount of heterogeneity accounted for):            0.00%
## 
## Test for Residual Heterogeneity:
## QE(df = 11) = 46.1159, p-val < .0001
## 
## Test of Moderators (coefficients 2:5):
## QM(df = 4) = 2.5698, p-val = 0.6322
## 
## Model Results:
## 
##                         estimate      se     zval    pval    ci.lb   ci.ub 
## intrcpt                  -0.3537  1.7923  -0.1974  0.8435  -3.8666  3.1592    
## continentEurope          -0.1268  0.4111  -0.3085  0.7577  -0.9326  0.6790    
## continentNorth America   -0.3145  1.3048  -0.2410  0.8095  -2.8718  2.2429    
## mean.age                  0.0030  0.0267   0.1139  0.9093  -0.0493  0.0554    
## scale                     0.0355  0.1143   0.3102  0.7564  -0.1885  0.2594    
## 
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

Age${ }^{2}$ effect

## 
## Mixed-Effects Model (k = 16; tau^2 estimator: REML)
## 
##   logLik  deviance       AIC       BIC      AICc 
##  27.7483  -55.4966  -43.4966  -41.1092  -22.4966   
## 
## tau^2 (estimated amount of residual heterogeneity):     0.0001 (SE = 0.0001)
## tau (square root of estimated tau^2 value):             0.0118
## I^2 (residual heterogeneity / unaccounted variability): 63.19%
## H^2 (unaccounted variability / sampling variability):   2.72
## R^2 (amount of heterogeneity accounted for):            47.49%
## 
## Test for Residual Heterogeneity:
## QE(df = 11) = 20.1757, p-val = 0.0430
## 
## Test of Moderators (coefficients 2:5):
## QM(df = 4) = 8.8971, p-val = 0.0637
## 
## Model Results:
## 
##                         estimate      se     zval    pval    ci.lb   ci.ub 
## intrcpt                  -0.4014  0.3870  -1.0373  0.2996  -1.1599  0.3570    
## continentEurope          -0.0564  0.0883  -0.6384  0.5232  -0.2295  0.1167    
## continentNorth America   -0.2837  0.2813  -1.0085  0.3132  -0.8350  0.2676    
## mean.age                  0.0054  0.0058   0.9303  0.3522  -0.0059  0.0167    
## scale                     0.0275  0.0246   1.1178  0.2637  -0.0207  0.0757    
## 
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

Quadratic with gender model

Meta analysis:
Age effect results

## 
## Random-Effects Model (k = 16; tau^2 estimator: REML)
## 
##   logLik  deviance       AIC       BIC      AICc 
##  15.2625  -30.5250  -26.5250  -25.1089  -25.5250   
## 
## tau^2 (estimated amount of total heterogeneity): 0.0045 (SE = 0.0024)
## tau (square root of estimated tau^2 value):      0.0669
## I^2 (total heterogeneity / total variability):   96.63%
## H^2 (total variability / sampling variability):  29.65
## 
## Test for Heterogeneity:
## Q(df = 15) = 112.2968, p-val < .0001
## 
## Model Results:
## 
## estimate      se     zval    pval    ci.lb    ci.ub 
##  -0.1293  0.0206  -6.2818  <.0001  -0.1697  -0.0890  *** 
## 
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

Age${ }^{2}$ effect

## 
## Random-Effects Model (k = 16; tau^2 estimator: REML)
## 
##   logLik  deviance       AIC       BIC      AICc 
##  37.5936  -75.1871  -71.1871  -69.7710  -70.1871   
## 
## tau^2 (estimated amount of total heterogeneity): 0.0003 (SE = 0.0001)
## tau (square root of estimated tau^2 value):      0.0159
## I^2 (total heterogeneity / total variability):   89.29%
## H^2 (total variability / sampling variability):  9.34
## 
## Test for Heterogeneity:
## Q(df = 15) = 328.8947, p-val < .0001
## 
## Model Results:
## 
## estimate      se    zval    pval    ci.lb   ci.ub 
##   0.0051  0.0051  1.0165  0.3094  -0.0048  0.0151    
## 
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

Gender effect results

## 
## Random-Effects Model (k = 16; tau^2 estimator: REML)
## 
##   logLik  deviance       AIC       BIC      AICc 
##  11.5046  -23.0092  -19.0092  -17.5931  -18.0092   
## 
## tau^2 (estimated amount of total heterogeneity): 0.0114 (SE = 0.0045)
## tau (square root of estimated tau^2 value):      0.1070
## I^2 (total heterogeneity / total variability):   95.44%
## H^2 (total variability / sampling variability):  21.91
## 
## Test for Heterogeneity:
## Q(df = 15) = 474.3101, p-val < .0001
## 
## Model Results:
## 
## estimate      se      zval    pval    ci.lb    ci.ub 
##  -0.2794  0.0278  -10.0336  <.0001  -0.3340  -0.2248  *** 
## 
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

Meta analysis with three moderators (continent, mean age, scale range):
Age effect results

## 
## Mixed-Effects Model (k = 16; tau^2 estimator: REML)
## 
##   logLik  deviance       AIC       BIC      AICc 
##  10.5264  -21.0528   -9.0528   -6.6655   11.9472   
## 
## tau^2 (estimated amount of residual heterogeneity):     0.0049 (SE = 0.0032)
## tau (square root of estimated tau^2 value):             0.0702
## I^2 (residual heterogeneity / unaccounted variability): 92.63%
## H^2 (unaccounted variability / sampling variability):   13.57
## R^2 (amount of heterogeneity accounted for):            0.00%
## 
## Test for Residual Heterogeneity:
## QE(df = 11) = 54.1748, p-val < .0001
## 
## Test of Moderators (coefficients 2:5):
## QM(df = 4) = 3.4258, p-val = 0.4892
## 
## Model Results:
## 
##                         estimate      se     zval    pval    ci.lb   ci.ub 
## intrcpt                  -0.7228  1.7705  -0.4082  0.6831  -4.1929  2.7473    
## continentEurope          -0.2234  0.4061  -0.5501  0.5822  -1.0194  0.5726    
## continentNorth America   -0.6150  1.2888  -0.4772  0.6332  -3.1411  1.9110    
## mean.age                  0.0083  0.0264   0.3161  0.7520  -0.0434  0.0601    
## scale                     0.0610  0.1129   0.5407  0.5887  -0.1602  0.2823    
## 
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

Age${ }^{2}$ effect

## 
## Mixed-Effects Model (k = 16; tau^2 estimator: REML)
## 
##   logLik  deviance       AIC       BIC      AICc 
##  27.9453  -55.8905  -43.8905  -41.5032  -22.8905   
## 
## tau^2 (estimated amount of residual heterogeneity):     0.0001 (SE = 0.0001)
## tau (square root of estimated tau^2 value):             0.0121
## I^2 (residual heterogeneity / unaccounted variability): 64.81%
## H^2 (unaccounted variability / sampling variability):   2.84
## R^2 (amount of heterogeneity accounted for):            42.63%
## 
## Test for Residual Heterogeneity:
## QE(df = 11) = 20.2787, p-val = 0.0417
## 
## Test of Moderators (coefficients 2:5):
## QM(df = 4) = 8.0294, p-val = 0.0905
## 
## Model Results:
## 
##                         estimate      se     zval    pval    ci.lb   ci.ub 
## intrcpt                  -0.2293  0.3868  -0.5929  0.5533  -0.9875  0.5288    
## continentEurope          -0.0144  0.0883  -0.1625  0.8709  -0.1875  0.1588    
## continentNorth America   -0.1489  0.2812  -0.5296  0.5964  -0.7000  0.4022    
## mean.age                  0.0029  0.0058   0.5002  0.6169  -0.0084  0.0142    
## scale                     0.0156  0.0246   0.6345  0.5258  -0.0326  0.0638    
## 
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

Gender effect results

## 
## Mixed-Effects Model (k = 16; tau^2 estimator: REML)
## 
##   logLik  deviance       AIC       BIC      AICc 
##  10.4347  -20.8693   -8.8693   -6.4819   12.1307   
## 
## tau^2 (estimated amount of residual heterogeneity):     0.0067 (SE = 0.0033)
## tau (square root of estimated tau^2 value):             0.0821
## I^2 (residual heterogeneity / unaccounted variability): 89.68%
## H^2 (unaccounted variability / sampling variability):   9.69
## R^2 (amount of heterogeneity accounted for):            41.16%
## 
## Test for Residual Heterogeneity:
## QE(df = 11) = 88.7805, p-val < .0001
## 
## Test of Moderators (coefficients 2:5):
## QM(df = 4) = 12.1736, p-val = 0.0161
## 
## Model Results:
## 
##                         estimate      se     zval    pval    ci.lb    ci.ub 
## intrcpt                  -3.1459  1.6873  -1.8644  0.0623  -6.4531   0.1612  . 
## continentEurope          -0.8839  0.3907  -2.2624  0.0237  -1.6496  -0.1182  * 
## continentNorth America   -2.3202  1.2334  -1.8811  0.0600  -4.7377   0.0972  . 
## mean.age                  0.0476  0.0251   1.8939  0.0582  -0.0017   0.0968  . 
## scale                     0.1648  0.1085   1.5188  0.1288  -0.0479   0.3774    
## 
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

5.3. Driving risk-taking

Intercept only model

Meta analysis:
ICC’s results

## 
## Random-Effects Model (k = 3; tau^2 estimator: REML)
## 
##   logLik  deviance       AIC       BIC      AICc 
##   2.5203   -5.0407   -1.0407   -3.6544   10.9593   
## 
## tau^2 (estimated amount of total heterogeneity): 0.0047 (SE = 0.0047)
## tau (square root of estimated tau^2 value):      0.0682
## I^2 (total heterogeneity / total variability):   98.87%
## H^2 (total variability / sampling variability):  88.61
## 
## Test for Heterogeneity:
## Q(df = 2) = 182.3171, p-val < .0001
## 
## Model Results:
## 
## estimate      se     zval    pval   ci.lb   ci.ub 
##   0.4669  0.0396  11.7828  <.0001  0.3892  0.5446  *** 
## 
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

Fixed effect model

Meta analysis:
Age effect results

## 
## Random-Effects Model (k = 3; tau^2 estimator: REML)
## 
##   logLik  deviance       AIC       BIC      AICc 
##   4.8352   -9.6704   -5.6704   -8.2841    6.3296   
## 
## tau^2 (estimated amount of total heterogeneity): 0.0004 (SE = 0.0005)
## tau (square root of estimated tau^2 value):      0.0207
## I^2 (total heterogeneity / total variability):   90.39%
## H^2 (total variability / sampling variability):  10.40
## 
## Test for Heterogeneity:
## Q(df = 2) = 26.7937, p-val < .0001
## 
## Model Results:
## 
## estimate      se     zval    pval    ci.lb    ci.ub 
##  -0.1033  0.0127  -8.1424  <.0001  -0.1282  -0.0784  *** 
## 
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

Linear model

Meta analysis:
Age effect results

## 
## Random-Effects Model (k = 3; tau^2 estimator: REML)
## 
##   logLik  deviance       AIC       BIC      AICc 
##   4.6366   -9.2733   -5.2733   -7.8870    6.7267   
## 
## tau^2 (estimated amount of total heterogeneity): 0.0005 (SE = 0.0006)
## tau (square root of estimated tau^2 value):      0.0231
## I^2 (total heterogeneity / total variability):   92.07%
## H^2 (total variability / sampling variability):  12.62
## 
## Test for Heterogeneity:
## Q(df = 2) = 32.6057, p-val < .0001
## 
## Model Results:
## 
## estimate      se     zval    pval    ci.lb    ci.ub 
##  -0.1032  0.0140  -7.3928  <.0001  -0.1306  -0.0759  *** 
## 
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

Linear with gender model

Meta analysis:
Age effect results

## 
## Random-Effects Model (k = 3; tau^2 estimator: REML)
## 
##   logLik  deviance       AIC       BIC      AICc 
##   4.5839   -9.1678   -5.1678   -7.7815    6.8322   
## 
## tau^2 (estimated amount of total heterogeneity): 0.0006 (SE = 0.0006)
## tau (square root of estimated tau^2 value):      0.0238
## I^2 (total heterogeneity / total variability):   92.85%
## H^2 (total variability / sampling variability):  13.98
## 
## Test for Heterogeneity:
## Q(df = 2) = 36.7307, p-val < .0001
## 
## Model Results:
## 
## estimate      se     zval    pval    ci.lb    ci.ub 
##  -0.1091  0.0143  -7.6161  <.0001  -0.1372  -0.0810  *** 
## 
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

Gender effect results

## 
## Random-Effects Model (k = 3; tau^2 estimator: REML)
## 
##   logLik  deviance       AIC       BIC      AICc 
##   2.8299   -5.6598   -1.6598   -4.2735   10.3402   
## 
## tau^2 (estimated amount of total heterogeneity): 0.0030 (SE = 0.0034)
## tau (square root of estimated tau^2 value):      0.0550
## I^2 (total heterogeneity / total variability):   90.70%
## H^2 (total variability / sampling variability):  10.75
## 
## Test for Heterogeneity:
## Q(df = 2) = 17.5281, p-val = 0.0002
## 
## Model Results:
## 
## estimate      se      zval    pval    ci.lb    ci.ub 
##  -0.3864  0.0335  -11.5326  <.0001  -0.4521  -0.3208  *** 
## 
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

Linear with gender interaction model

Meta analysis:
Age effect results

## 
## Random-Effects Model (k = 3; tau^2 estimator: REML)
## 
##   logLik  deviance       AIC       BIC      AICc 
##   4.8824   -9.7648   -5.7648   -8.3786    6.2352   
## 
## tau^2 (estimated amount of total heterogeneity): 0.0003 (SE = 0.0005)
## tau (square root of estimated tau^2 value):      0.0186
## I^2 (total heterogeneity / total variability):   79.04%
## H^2 (total variability / sampling variability):  4.77
## 
## Test for Heterogeneity:
## Q(df = 2) = 10.1851, p-val = 0.0061
## 
## Model Results:
## 
## estimate      se     zval    pval    ci.lb    ci.ub 
##  -0.1213  0.0122  -9.9249  <.0001  -0.1453  -0.0974  *** 
## 
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

Gender effect results

## 
## Random-Effects Model (k = 3; tau^2 estimator: REML)
## 
##   logLik  deviance       AIC       BIC      AICc 
##   3.1469   -6.2938   -2.2938   -4.9075    9.7062   
## 
## tau^2 (estimated amount of total heterogeneity): 0.0021 (SE = 0.0028)
## tau (square root of estimated tau^2 value):      0.0455
## I^2 (total heterogeneity / total variability):   78.37%
## H^2 (total variability / sampling variability):  4.62
## 
## Test for Heterogeneity:
## Q(df = 2) = 11.3390, p-val = 0.0034
## 
## Model Results:
## 
## estimate      se      zval    pval    ci.lb    ci.ub 
##  -0.3905  0.0304  -12.8503  <.0001  -0.4501  -0.3310  *** 
## 
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

Age $\times$ Gender effect results

## 
## Random-Effects Model (k = 3; tau^2 estimator: REML)
## 
##   logLik  deviance       AIC       BIC      AICc 
##   3.9514   -7.9028   -3.9028   -6.5165    8.0972   
## 
## tau^2 (estimated amount of total heterogeneity): 0.0009 (SE = 0.0011)
## tau (square root of estimated tau^2 value):      0.0295
## I^2 (total heterogeneity / total variability):   83.06%
## H^2 (total variability / sampling variability):  5.90
## 
## Test for Heterogeneity:
## Q(df = 2) = 10.0802, p-val = 0.0065
## 
## Model Results:
## 
## estimate      se    zval    pval    ci.lb   ci.ub 
##   0.0223  0.0188  1.1853  0.2359  -0.0146  0.0593    
## 
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

Quadratic model

Meta analysis:
Age effect results

## 
## Random-Effects Model (k = 2; tau^2 estimator: REML)
## 
##   logLik  deviance       AIC       BIC      AICc 
##   2.4836   -4.9671   -0.9671   -4.9671   11.0329   
## 
## tau^2 (estimated amount of total heterogeneity): 0 (SE = 0.0011)
## tau (square root of estimated tau^2 value):      0
## I^2 (total heterogeneity / total variability):   0.00%
## H^2 (total variability / sampling variability):  1.00
## 
## Test for Heterogeneity:
## Q(df = 1) = 0.3560, p-val = 0.5507
## 
## Model Results:
## 
## estimate      se      zval    pval    ci.lb    ci.ub 
##  -0.0922  0.0081  -11.4296  <.0001  -0.1080  -0.0764  *** 
## 
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

Age${ }^{2}$ effect

## 
## Random-Effects Model (k = 2; tau^2 estimator: REML)
## 
##   logLik  deviance       AIC       BIC      AICc 
##   3.3224   -6.6449   -2.6449   -6.6449    9.3551   
## 
## tau^2 (estimated amount of total heterogeneity): 0.0000 (SE = 0.0001)
## tau (square root of estimated tau^2 value):      0.0049
## I^2 (total heterogeneity / total variability):   31.56%
## H^2 (total variability / sampling variability):  1.46
## 
## Test for Heterogeneity:
## Q(df = 1) = 1.4612, p-val = 0.2267
## 
## Model Results:
## 
## estimate      se    zval    pval   ci.lb   ci.ub 
##   0.0125  0.0056  2.2359  0.0254  0.0015  0.0234  * 
## 
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

Quadratic with gender model

Meta analysis:
Age effect results

## 
## Random-Effects Model (k = 2; tau^2 estimator: REML)
## 
##   logLik  deviance       AIC       BIC      AICc 
##   2.1199   -4.2398   -0.2398   -4.2398   11.7602   
## 
## tau^2 (estimated amount of total heterogeneity): 0.0001 (SE = 0.0012)
## tau (square root of estimated tau^2 value):      0.0099
## I^2 (total heterogeneity / total variability):   11.63%
## H^2 (total variability / sampling variability):  1.13
## 
## Test for Heterogeneity:
## Q(df = 1) = 1.1316, p-val = 0.2874
## 
## Model Results:
## 
## estimate      se     zval    pval    ci.lb    ci.ub 
##  -0.1009  0.0121  -8.3189  <.0001  -0.1247  -0.0771  *** 
## 
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

Age${ }^{2}$ effect

## 
## Random-Effects Model (k = 2; tau^2 estimator: REML)
## 
##   logLik  deviance       AIC       BIC      AICc 
##   3.8099   -7.6199   -3.6199   -7.6199    8.3801   
## 
## tau^2 (estimated amount of total heterogeneity): 0 (SE = 0.0001)
## tau (square root of estimated tau^2 value):      0
## I^2 (total heterogeneity / total variability):   0.00%
## H^2 (total variability / sampling variability):  1.00
## 
## Test for Heterogeneity:
## Q(df = 1) = 0.4464, p-val = 0.5040
## 
## Model Results:
## 
## estimate      se    zval    pval   ci.lb   ci.ub 
##   0.0140  0.0039  3.5778  0.0003  0.0063  0.0216  *** 
## 
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

Gender effect results

## 
## Random-Effects Model (k = 2; tau^2 estimator: REML)
## 
##   logLik  deviance       AIC       BIC      AICc 
##   1.3474   -2.6949    1.3051   -2.6949   13.3051   
## 
## tau^2 (estimated amount of total heterogeneity): 0.0035 (SE = 0.0056)
## tau (square root of estimated tau^2 value):      0.0592
## I^2 (total heterogeneity / total variability):   88.73%
## H^2 (total variability / sampling variability):  8.87
## 
## Test for Heterogeneity:
## Q(df = 1) = 8.8744, p-val = 0.0029
## 
## Model Results:
## 
## estimate      se     zval    pval    ci.lb    ci.ub 
##  -0.3622  0.0444  -8.1494  <.0001  -0.4493  -0.2751  *** 
## 
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

5.4. Recreational risk-taking

Intercept only model

Meta analysis:
ICC’s results

## 
## Random-Effects Model (k = 3; tau^2 estimator: REML)
## 
##   logLik  deviance       AIC       BIC      AICc 
##   3.2644   -6.5288   -2.5288   -5.1425    9.4712   
## 
## tau^2 (estimated amount of total heterogeneity): 0.0022 (SE = 0.0022)
## tau (square root of estimated tau^2 value):      0.0470
## I^2 (total heterogeneity / total variability):   98.58%
## H^2 (total variability / sampling variability):  70.47
## 
## Test for Heterogeneity:
## Q(df = 2) = 157.3650, p-val < .0001
## 
## Model Results:
## 
## estimate      se     zval    pval   ci.lb   ci.ub 
##   0.4704  0.0273  17.2074  <.0001  0.4168  0.5240  *** 
## 
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

Fixed effect model

Meta analysis:
Age effect results

## 
## Random-Effects Model (k = 3; tau^2 estimator: REML)
## 
##   logLik  deviance       AIC       BIC      AICc 
##   3.5973   -7.1946   -3.1946   -5.8083    8.8054   
## 
## tau^2 (estimated amount of total heterogeneity): 0.0016 (SE = 0.0016)
## tau (square root of estimated tau^2 value):      0.0396
## I^2 (total heterogeneity / total variability):   97.01%
## H^2 (total variability / sampling variability):  33.48
## 
## Test for Heterogeneity:
## Q(df = 2) = 91.2519, p-val < .0001
## 
## Model Results:
## 
## estimate      se     zval    pval    ci.lb    ci.ub 
##  -0.1667  0.0233  -7.1603  <.0001  -0.2124  -0.1211  *** 
## 
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

Linear model

Meta analysis:
Age effect results

## 
## Random-Effects Model (k = 3; tau^2 estimator: REML)
## 
##   logLik  deviance       AIC       BIC      AICc 
##   3.5134   -7.0269   -3.0269   -5.6406    8.9731   
## 
## tau^2 (estimated amount of total heterogeneity): 0.0017 (SE = 0.0018)
## tau (square root of estimated tau^2 value):      0.0413
## I^2 (total heterogeneity / total variability):   97.28%
## H^2 (total variability / sampling variability):  36.73
## 
## Test for Heterogeneity:
## Q(df = 2) = 102.4067, p-val < .0001
## 
## Model Results:
## 
## estimate      se     zval    pval    ci.lb    ci.ub 
##  -0.1643  0.0243  -6.7657  <.0001  -0.2119  -0.1167  *** 
## 
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

Linear with gender model

Meta analysis:
Age effect results

## 
## Random-Effects Model (k = 3; tau^2 estimator: REML)
## 
##   logLik  deviance       AIC       BIC      AICc 
##   3.6276   -7.2551   -3.2551   -5.8688    8.7449   
## 
## tau^2 (estimated amount of total heterogeneity): 0.0015 (SE = 0.0016)
## tau (square root of estimated tau^2 value):      0.0390
## I^2 (total heterogeneity / total variability):   97.07%
## H^2 (total variability / sampling variability):  34.13
## 
## Test for Heterogeneity:
## Q(df = 2) = 94.9308, p-val < .0001
## 
## Model Results:
## 
## estimate      se     zval    pval    ci.lb    ci.ub 
##  -0.1685  0.0229  -7.3422  <.0001  -0.2134  -0.1235  *** 
## 
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

Gender effect results

## 
## Random-Effects Model (k = 3; tau^2 estimator: REML)
## 
##   logLik  deviance       AIC       BIC      AICc 
##   2.7595   -5.5190   -1.5190   -4.1327   10.4810   
## 
## tau^2 (estimated amount of total heterogeneity): 0.0033 (SE = 0.0036)
## tau (square root of estimated tau^2 value):      0.0571
## I^2 (total heterogeneity / total variability):   90.72%
## H^2 (total variability / sampling variability):  10.78
## 
## Test for Heterogeneity:
## Q(df = 2) = 17.8857, p-val = 0.0001
## 
## Model Results:
## 
## estimate      se      zval    pval    ci.lb    ci.ub 
##  -0.3723  0.0347  -10.7146  <.0001  -0.4403  -0.3042  *** 
## 
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

Linear with gender interaction model

Meta analysis:
Age effect results

## 
## Random-Effects Model (k = 3; tau^2 estimator: REML)
## 
##   logLik  deviance       AIC       BIC      AICc 
##   3.2003   -6.4006   -2.4006   -5.0143    9.5994   
## 
## tau^2 (estimated amount of total heterogeneity): 0.0023 (SE = 0.0024)
## tau (square root of estimated tau^2 value):      0.0477
## I^2 (total heterogeneity / total variability):   95.90%
## H^2 (total variability / sampling variability):  24.39
## 
## Test for Heterogeneity:
## Q(df = 2) = 55.6030, p-val < .0001
## 
## Model Results:
## 
## estimate      se     zval    pval    ci.lb    ci.ub 
##  -0.1799  0.0283  -6.3562  <.0001  -0.2354  -0.1244  *** 
## 
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

Gender effect results

## 
## Random-Effects Model (k = 3; tau^2 estimator: REML)
## 
##   logLik  deviance       AIC       BIC      AICc 
##   4.5275   -9.0549   -5.0549   -7.6686    6.9451   
## 
## tau^2 (estimated amount of total heterogeneity): 0 (SE = 0.0005)
## tau (square root of estimated tau^2 value):      0
## I^2 (total heterogeneity / total variability):   0.00%
## H^2 (total variability / sampling variability):  1.00
## 
## Test for Heterogeneity:
## Q(df = 2) = 1.6995, p-val = 0.4275
## 
## Model Results:
## 
## estimate      se      zval    pval    ci.lb    ci.ub 
##  -0.3623  0.0110  -33.0510  <.0001  -0.3838  -0.3408  *** 
## 
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

Age $\times$ Gender effect results

## 
## Random-Effects Model (k = 3; tau^2 estimator: REML)
## 
##   logLik  deviance       AIC       BIC      AICc 
##   3.7081   -7.4162   -3.4162   -6.0300    8.5838   
## 
## tau^2 (estimated amount of total heterogeneity): 0.0011 (SE = 0.0013)
## tau (square root of estimated tau^2 value):      0.0330
## I^2 (total heterogeneity / total variability):   85.37%
## H^2 (total variability / sampling variability):  6.84
## 
## Test for Heterogeneity:
## Q(df = 2) = 9.1604, p-val = 0.0103
## 
## Model Results:
## 
## estimate      se    zval    pval    ci.lb   ci.ub 
##   0.0255  0.0209  1.2200  0.2224  -0.0154  0.0663    
## 
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

Quadratic model

Meta analysis:
Age effect results

## 
## Random-Effects Model (k = 2; tau^2 estimator: REML)
## 
##   logLik  deviance       AIC       BIC      AICc 
##   1.2358   -2.4716    1.5284   -2.4716   13.5284   
## 
## tau^2 (estimated amount of total heterogeneity): 0.0041 (SE = 0.0070)
## tau (square root of estimated tau^2 value):      0.0637
## I^2 (total heterogeneity / total variability):   82.13%
## H^2 (total variability / sampling variability):  5.59
## 
## Test for Heterogeneity:
## Q(df = 1) = 5.5946, p-val = 0.0180
## 
## Model Results:
## 
## estimate      se     zval    pval    ci.lb    ci.ub 
##  -0.1150  0.0490  -2.3456  0.0190  -0.2111  -0.0189  * 
## 
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

Age${ }^{2}$ effect

## 
## Random-Effects Model (k = 2; tau^2 estimator: REML)
## 
##   logLik  deviance       AIC       BIC      AICc 
##   1.8503   -3.7006    0.2994   -3.7006   12.2994   
## 
## tau^2 (estimated amount of total heterogeneity): 0.0014 (SE = 0.0020)
## tau (square root of estimated tau^2 value):      0.0372
## I^2 (total heterogeneity / total variability):   95.87%
## H^2 (total variability / sampling variability):  24.23
## 
## Test for Heterogeneity:
## Q(df = 1) = 24.2273, p-val < .0001
## 
## Model Results:
## 
## estimate      se    zval    pval    ci.lb   ci.ub 
##   0.0057  0.0269  0.2125  0.8317  -0.0470  0.0584    
## 
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

Quadratic with gender model

Meta analysis:
Age effect results

## 
## Random-Effects Model (k = 2; tau^2 estimator: REML)
## 
##   logLik  deviance       AIC       BIC      AICc 
##   1.4810   -2.9620    1.0380   -2.9620   13.0380   
## 
## tau^2 (estimated amount of total heterogeneity): 0.0022 (SE = 0.0043)
## tau (square root of estimated tau^2 value):      0.0467
## I^2 (total heterogeneity / total variability):   71.97%
## H^2 (total variability / sampling variability):  3.57
## 
## Test for Heterogeneity:
## Q(df = 1) = 3.5676, p-val = 0.0589
## 
## Model Results:
## 
## estimate      se     zval    pval    ci.lb    ci.ub 
##  -0.1321  0.0376  -3.5157  0.0004  -0.2058  -0.0585  *** 
## 
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

Age${ }^{2}$ effect

## 
## Random-Effects Model (k = 2; tau^2 estimator: REML)
## 
##   logLik  deviance       AIC       BIC      AICc 
##   1.9506   -3.9012    0.0988   -3.9012   12.0988   
## 
## tau^2 (estimated amount of total heterogeneity): 0.0011 (SE = 0.0017)
## tau (square root of estimated tau^2 value):      0.0336
## I^2 (total heterogeneity / total variability):   95.16%
## H^2 (total variability / sampling variability):  20.66
## 
## Test for Heterogeneity:
## Q(df = 1) = 20.6555, p-val < .0001
## 
## Model Results:
## 
## estimate      se    zval    pval    ci.lb   ci.ub 
##   0.0083  0.0243  0.3429  0.7317  -0.0393  0.0560    
## 
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

Gender effect results

## 
## Random-Effects Model (k = 2; tau^2 estimator: REML)
## 
##   logLik  deviance       AIC       BIC      AICc 
##   1.0458   -2.0917    1.9083   -2.0917   13.9083   
## 
## tau^2 (estimated amount of total heterogeneity): 0.0067 (SE = 0.0102)
## tau (square root of estimated tau^2 value):      0.0822
## I^2 (total heterogeneity / total variability):   93.35%
## H^2 (total variability / sampling variability):  15.04
## 
## Test for Heterogeneity:
## Q(df = 1) = 15.0437, p-val = 0.0001
## 
## Model Results:
## 
## estimate      se     zval    pval    ci.lb    ci.ub 
##  -0.3781  0.0601  -6.2896  <.0001  -0.4959  -0.2603  *** 
## 
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

5.5. Occupational risk-taking

Intercept only model

Meta analysis:
ICC’s results

## 
## Random-Effects Model (k = 3; tau^2 estimator: REML)
## 
##   logLik  deviance       AIC       BIC      AICc 
##   2.7906   -5.5812   -1.5812   -4.1949   10.4188   
## 
## tau^2 (estimated amount of total heterogeneity): 0.0035 (SE = 0.0036)
## tau (square root of estimated tau^2 value):      0.0595
## I^2 (total heterogeneity / total variability):   98.56%
## H^2 (total variability / sampling variability):  69.50
## 
## Test for Heterogeneity:
## Q(df = 2) = 137.3340, p-val < .0001
## 
## Model Results:
## 
## estimate      se     zval    pval   ci.lb   ci.ub 
##   0.4103  0.0346  11.8558  <.0001  0.3425  0.4781  *** 
## 
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

Fixed effect model

Meta analysis:
Age effect results

## 
## Random-Effects Model (k = 3; tau^2 estimator: REML)
## 
##   logLik  deviance       AIC       BIC      AICc 
##   4.9206   -9.8412   -5.8412   -8.4549    6.1588   
## 
## tau^2 (estimated amount of total heterogeneity): 0.0004 (SE = 0.0005)
## tau (square root of estimated tau^2 value):      0.0197
## I^2 (total heterogeneity / total variability):   87.96%
## H^2 (total variability / sampling variability):  8.30
## 
## Test for Heterogeneity:
## Q(df = 2) = 21.5199, p-val < .0001
## 
## Model Results:
## 
## estimate      se      zval    pval    ci.lb    ci.ub 
##  -0.1719  0.0122  -14.0513  <.0001  -0.1959  -0.1480  *** 
## 
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

Linear model

Meta analysis:
Age effect results

## 
## Random-Effects Model (k = 3; tau^2 estimator: REML)
## 
##   logLik  deviance       AIC       BIC      AICc 
##   5.0252  -10.0503   -6.0503   -8.6640    5.9497   
## 
## tau^2 (estimated amount of total heterogeneity): 0.0003 (SE = 0.0004)
## tau (square root of estimated tau^2 value):      0.0185
## I^2 (total heterogeneity / total variability):   86.71%
## H^2 (total variability / sampling variability):  7.53
## 
## Test for Heterogeneity:
## Q(df = 2) = 19.2449, p-val < .0001
## 
## Model Results:
## 
## estimate      se      zval    pval    ci.lb    ci.ub 
##  -0.1718  0.0116  -14.7734  <.0001  -0.1946  -0.1490  *** 
## 
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

Linear with gender model

Meta analysis:
Age effect results

## 
## Random-Effects Model (k = 3; tau^2 estimator: REML)
## 
##   logLik  deviance       AIC       BIC      AICc 
##   5.2083  -10.4166   -6.4166   -9.0303    5.5834   
## 
## tau^2 (estimated amount of total heterogeneity): 0.0003 (SE = 0.0003)
## tau (square root of estimated tau^2 value):      0.0168
## I^2 (total heterogeneity / total variability):   84.60%
## H^2 (total variability / sampling variability):  6.49
## 
## Test for Heterogeneity:
## Q(df = 2) = 16.4534, p-val = 0.0003
## 
## Model Results:
## 
## estimate      se      zval    pval    ci.lb    ci.ub 
##  -0.1759  0.0107  -16.4728  <.0001  -0.1968  -0.1550  *** 
## 
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

Gender effect results

## 
## Random-Effects Model (k = 3; tau^2 estimator: REML)
## 
##   logLik  deviance       AIC       BIC      AICc 
##   2.8421   -5.6842   -1.6842   -4.2979   10.3158   
## 
## tau^2 (estimated amount of total heterogeneity): 0.0029 (SE = 0.0033)
## tau (square root of estimated tau^2 value):      0.0542
## I^2 (total heterogeneity / total variability):   89.39%
## H^2 (total variability / sampling variability):  9.43
## 
## Test for Heterogeneity:
## Q(df = 2) = 15.1697, p-val = 0.0005
## 
## Model Results:
## 
## estimate      se     zval    pval    ci.lb    ci.ub 
##  -0.2676  0.0332  -8.0552  <.0001  -0.3327  -0.2025  *** 
## 
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

Linear with gender interaction model

Meta analysis:
Age effect results

## 
## Random-Effects Model (k = 3; tau^2 estimator: REML)
## 
##   logLik  deviance       AIC       BIC      AICc 
##   4.1667   -8.3333   -4.3333   -6.9471    7.6667   
## 
## tau^2 (estimated amount of total heterogeneity): 0.0007 (SE = 0.0008)
## tau (square root of estimated tau^2 value):      0.0265
## I^2 (total heterogeneity / total variability):   86.97%
## H^2 (total variability / sampling variability):  7.67
## 
## Test for Heterogeneity:
## Q(df = 2) = 10.5567, p-val = 0.0051
## 
## Model Results:
## 
## estimate      se      zval    pval    ci.lb    ci.ub 
##  -0.1679  0.0167  -10.0754  <.0001  -0.2006  -0.1352  *** 
## 
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

Gender effect results

## 
## Random-Effects Model (k = 3; tau^2 estimator: REML)
## 
##   logLik  deviance       AIC       BIC      AICc 
##   2.5565   -5.1131   -1.1131   -3.7268   10.8869   
## 
## tau^2 (estimated amount of total heterogeneity): 0.0039 (SE = 0.0048)
## tau (square root of estimated tau^2 value):      0.0625
## I^2 (total heterogeneity / total variability):   87.12%
## H^2 (total variability / sampling variability):  7.76
## 
## Test for Heterogeneity:
## Q(df = 2) = 18.7875, p-val < .0001
## 
## Model Results:
## 
## estimate      se     zval    pval    ci.lb    ci.ub 
##  -0.2323  0.0397  -5.8503  <.0001  -0.3101  -0.1545  *** 
## 
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

Age $\times$ Gender effect results

## 
## Random-Effects Model (k = 3; tau^2 estimator: REML)
## 
##   logLik  deviance       AIC       BIC      AICc 
##   3.1625   -6.3251   -2.3251   -4.9388    9.6749   
## 
## tau^2 (estimated amount of total heterogeneity): 0.0021 (SE = 0.0024)
## tau (square root of estimated tau^2 value):      0.0460
## I^2 (total heterogeneity / total variability):   91.02%
## H^2 (total variability / sampling variability):  11.14
## 
## Test for Heterogeneity:
## Q(df = 2) = 15.2978, p-val = 0.0005
## 
## Model Results:
## 
## estimate      se     zval    pval    ci.lb   ci.ub 
##  -0.0125  0.0281  -0.4464  0.6553  -0.0675  0.0425    
## 
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

Quadratic model

Meta analysis:
Age effect results

## 
## Random-Effects Model (k = 2; tau^2 estimator: REML)
## 
##   logLik  deviance       AIC       BIC      AICc 
##   1.9747   -3.9494    0.0506   -3.9494   12.0506   
## 
## tau^2 (estimated amount of total heterogeneity): 0.0001 (SE = 0.0016)
## tau (square root of estimated tau^2 value):      0.0117
## I^2 (total heterogeneity / total variability):   12.09%
## H^2 (total variability / sampling variability):  1.14
## 
## Test for Heterogeneity:
## Q(df = 1) = 1.1375, p-val = 0.2862
## 
## Model Results:
## 
## estimate      se      zval    pval    ci.lb    ci.ub 
##  -0.1592  0.0134  -11.8399  <.0001  -0.1856  -0.1329  *** 
## 
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

Age${ }^{2}$ effect

## 
## Random-Effects Model (k = 2; tau^2 estimator: REML)
## 
##   logLik  deviance       AIC       BIC      AICc 
##   2.3943   -4.7886   -0.7886   -4.7886   11.2114   
## 
## tau^2 (estimated amount of total heterogeneity): 0.0004 (SE = 0.0007)
## tau (square root of estimated tau^2 value):      0.0205
## I^2 (total heterogeneity / total variability):   85.89%
## H^2 (total variability / sampling variability):  7.09
## 
## Test for Heterogeneity:
## Q(df = 1) = 7.0884, p-val = 0.0078
## 
## Model Results:
## 
## estimate      se     zval    pval    ci.lb   ci.ub 
##  -0.0066  0.0155  -0.4252  0.6707  -0.0371  0.0238    
## 
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

Quadratic with gender model

Meta analysis:
Age effect results

## 
## Random-Effects Model (k = 2; tau^2 estimator: REML)
## 
##   logLik  deviance       AIC       BIC      AICc 
##   1.7685   -3.5370    0.4630   -3.5370   12.4630   
## 
## tau^2 (estimated amount of total heterogeneity): 0.0007 (SE = 0.0024)
## tau (square root of estimated tau^2 value):      0.0270
## I^2 (total heterogeneity / total variability):   42.83%
## H^2 (total variability / sampling variability):  1.75
## 
## Test for Heterogeneity:
## Q(df = 1) = 1.7490, p-val = 0.1860
## 
## Model Results:
## 
## estimate      se     zval    pval    ci.lb    ci.ub 
##  -0.1728  0.0246  -7.0122  <.0001  -0.2211  -0.1245  *** 
## 
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

Age${ }^{2}$ effect

## 
## Random-Effects Model (k = 2; tau^2 estimator: REML)
## 
##   logLik  deviance       AIC       BIC      AICc 
##   2.2911   -4.5823   -0.5823   -4.5823   11.4177   
## 
## tau^2 (estimated amount of total heterogeneity): 0.0005 (SE = 0.0008)
## tau (square root of estimated tau^2 value):      0.0231
## I^2 (total heterogeneity / total variability):   88.79%
## H^2 (total variability / sampling variability):  8.92
## 
## Test for Heterogeneity:
## Q(df = 1) = 8.9219, p-val = 0.0028
## 
## Model Results:
## 
## estimate      se     zval    pval    ci.lb   ci.ub 
##  -0.0060  0.0173  -0.3497  0.7266  -0.0399  0.0278    
## 
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

Gender effect results

## 
## Random-Effects Model (k = 2; tau^2 estimator: REML)
## 
##   logLik  deviance       AIC       BIC      AICc 
##   1.2096   -2.4193    1.5807   -2.4193   13.5807   
## 
## tau^2 (estimated amount of total heterogeneity): 0.0047 (SE = 0.0074)
## tau (square root of estimated tau^2 value):      0.0687
## I^2 (total heterogeneity / total variability):   90.66%
## H^2 (total variability / sampling variability):  10.71
## 
## Test for Heterogeneity:
## Q(df = 1) = 10.7067, p-val = 0.0011
## 
## Model Results:
## 
## estimate      se     zval    pval    ci.lb    ci.ub 
##  -0.2531  0.0510  -4.9602  <.0001  -0.3532  -0.1531  *** 
## 
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

5.6. Health risk-taking

Intercept only model

Meta analysis:
ICC’s results

## 
## Random-Effects Model (k = 3; tau^2 estimator: REML)
## 
##   logLik  deviance       AIC       BIC      AICc 
##   3.0547   -6.1095   -2.1095   -4.7232    9.8905   
## 
## tau^2 (estimated amount of total heterogeneity): 0.0027 (SE = 0.0027)
## tau (square root of estimated tau^2 value):      0.0519
## I^2 (total heterogeneity / total variability):   98.22%
## H^2 (total variability / sampling variability):  56.03
## 
## Test for Heterogeneity:
## Q(df = 2) = 93.0532, p-val < .0001
## 
## Model Results:
## 
## estimate      se     zval    pval   ci.lb   ci.ub 
##   0.3856  0.0303  12.7376  <.0001  0.3263  0.4450  *** 
## 
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

Fixed effect model

Meta analysis:
Age effect results

## 
## Random-Effects Model (k = 3; tau^2 estimator: REML)
## 
##   logLik  deviance       AIC       BIC      AICc 
##   3.6466   -7.2932   -3.2932   -5.9069    8.7068   
## 
## tau^2 (estimated amount of total heterogeneity): 0.0015 (SE = 0.0015)
## tau (square root of estimated tau^2 value):      0.0386
## I^2 (total heterogeneity / total variability):   97.29%
## H^2 (total variability / sampling variability):  36.93
## 
## Test for Heterogeneity:
## Q(df = 2) = 95.7654, p-val < .0001
## 
## Model Results:
## 
## estimate      se     zval    pval    ci.lb    ci.ub 
##  -0.0830  0.0227  -3.6591  0.0003  -0.1274  -0.0385  *** 
## 
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

Linear model

Meta analysis:
Age effect results

## 
## Random-Effects Model (k = 3; tau^2 estimator: REML)
## 
##   logLik  deviance       AIC       BIC      AICc 
##   3.6205   -7.2410   -3.2410   -5.8547    8.7590   
## 
## tau^2 (estimated amount of total heterogeneity): 0.0015 (SE = 0.0016)
## tau (square root of estimated tau^2 value):      0.0391
## I^2 (total heterogeneity / total variability):   97.37%
## H^2 (total variability / sampling variability):  38.02
## 
## Test for Heterogeneity:
## Q(df = 2) = 99.0488, p-val < .0001
## 
## Model Results:
## 
## estimate      se     zval    pval    ci.lb    ci.ub 
##  -0.0835  0.0230  -3.6326  0.0003  -0.1285  -0.0384  *** 
## 
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

Linear with gender model

Meta analysis:
Age effect results

## 
## Random-Effects Model (k = 3; tau^2 estimator: REML)
## 
##   logLik  deviance       AIC       BIC      AICc 
##   3.6806   -7.3611   -3.3611   -5.9748    8.6389   
## 
## tau^2 (estimated amount of total heterogeneity): 0.0014 (SE = 0.0015)
## tau (square root of estimated tau^2 value):      0.0379
## I^2 (total heterogeneity / total variability):   97.26%
## H^2 (total variability / sampling variability):  36.44
## 
## Test for Heterogeneity:
## Q(df = 2) = 94.0062, p-val < .0001
## 
## Model Results:
## 
## estimate      se     zval    pval    ci.lb    ci.ub 
##  -0.0852  0.0223  -3.8207  0.0001  -0.1289  -0.0415  *** 
## 
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

Gender effect results

## 
## Random-Effects Model (k = 3; tau^2 estimator: REML)
## 
##   logLik  deviance       AIC       BIC      AICc 
##   3.2578   -6.5156   -2.5156   -5.1293    9.4844   
## 
## tau^2 (estimated amount of total heterogeneity): 0.0019 (SE = 0.0023)
## tau (square root of estimated tau^2 value):      0.0439
## I^2 (total heterogeneity / total variability):   86.45%
## H^2 (total variability / sampling variability):  7.38
## 
## Test for Heterogeneity:
## Q(df = 2) = 15.0488, p-val = 0.0005
## 
## Model Results:
## 
## estimate      se     zval    pval    ci.lb    ci.ub 
##  -0.2472  0.0274  -9.0172  <.0001  -0.3009  -0.1935  *** 
## 
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

Linear with gender interaction model

Meta analysis:
Age effect results

## 
## Random-Effects Model (k = 3; tau^2 estimator: REML)
## 
##   logLik  deviance       AIC       BIC      AICc 
##   3.5915   -7.1831   -3.1831   -5.7968    8.8169   
## 
## tau^2 (estimated amount of total heterogeneity): 0.0015 (SE = 0.0017)
## tau (square root of estimated tau^2 value):      0.0393
## I^2 (total heterogeneity / total variability):   94.73%
## H^2 (total variability / sampling variability):  18.98
## 
## Test for Heterogeneity:
## Q(df = 2) = 52.2869, p-val < .0001
## 
## Model Results:
## 
## estimate      se     zval    pval    ci.lb    ci.ub 
##  -0.0907  0.0235  -3.8545  0.0001  -0.1368  -0.0446  *** 
## 
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

Gender effect results

## 
## Random-Effects Model (k = 3; tau^2 estimator: REML)
## 
##   logLik  deviance       AIC       BIC      AICc 
##   2.5542   -5.1085   -1.1085   -3.7222   10.8915   
## 
## tau^2 (estimated amount of total heterogeneity): 0.0038 (SE = 0.0046)
## tau (square root of estimated tau^2 value):      0.0619
## I^2 (total heterogeneity / total variability):   88.11%
## H^2 (total variability / sampling variability):  8.41
## 
## Test for Heterogeneity:
## Q(df = 2) = 18.3569, p-val = 0.0001
## 
## Model Results:
## 
## estimate      se     zval    pval    ci.lb    ci.ub 
##  -0.2313  0.0391  -5.9189  <.0001  -0.3078  -0.1547  *** 
## 
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

Age $\times$ Gender effect results

## 
## Random-Effects Model (k = 3; tau^2 estimator: REML)
## 
##   logLik  deviance       AIC       BIC      AICc 
##   3.3665   -6.7329   -2.7329   -5.3467    9.2671   
## 
## tau^2 (estimated amount of total heterogeneity): 0.0017 (SE = 0.0019)
## tau (square root of estimated tau^2 value):      0.0412
## I^2 (total heterogeneity / total variability):   91.15%
## H^2 (total variability / sampling variability):  11.31
## 
## Test for Heterogeneity:
## Q(df = 2) = 13.4856, p-val = 0.0012
## 
## Model Results:
## 
## estimate      se    zval    pval    ci.lb   ci.ub 
##   0.0143  0.0252  0.5671  0.5706  -0.0351  0.0636    
## 
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

Quadratic model

Meta analysis:
Age effect results

## 
## Random-Effects Model (k = 2; tau^2 estimator: REML)
## 
##   logLik  deviance       AIC       BIC      AICc 
##   1.7350   -3.4701    0.5299   -3.4701   12.5299   
## 
## tau^2 (estimated amount of total heterogeneity): 0.0010 (SE = 0.0026)
## tau (square root of estimated tau^2 value):      0.0313
## I^2 (total heterogeneity / total variability):   53.72%
## H^2 (total variability / sampling variability):  2.16
## 
## Test for Heterogeneity:
## Q(df = 1) = 2.1607, p-val = 0.1416
## 
## Model Results:
## 
## estimate      se     zval    pval    ci.lb    ci.ub 
##  -0.0604  0.0272  -2.2214  0.0263  -0.1137  -0.0071  * 
## 
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

Age${ }^{2}$ effect

## 
## Random-Effects Model (k = 2; tau^2 estimator: REML)
## 
##   logLik  deviance       AIC       BIC      AICc 
##   3.9445   -7.8890   -3.8890   -7.8890    8.1110   
## 
## tau^2 (estimated amount of total heterogeneity): 0 (SE = 0.0001)
## tau (square root of estimated tau^2 value):      0
## I^2 (total heterogeneity / total variability):   0.00%
## H^2 (total variability / sampling variability):  1.00
## 
## Test for Heterogeneity:
## Q(df = 1) = 0.0694, p-val = 0.7922
## 
## Model Results:
## 
## estimate      se    zval    pval    ci.lb   ci.ub 
##   0.0053  0.0037  1.4362  0.1510  -0.0019  0.0125    
## 
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

Quadratic with gender model

Meta analysis:
Age effect results

## 
## Random-Effects Model (k = 2; tau^2 estimator: REML)
## 
##   logLik  deviance       AIC       BIC      AICc 
##   1.5362   -3.0724    0.9276   -3.0724   12.9276   
## 
## tau^2 (estimated amount of total heterogeneity): 0.0019 (SE = 0.0038)
## tau (square root of estimated tau^2 value):      0.0433
## I^2 (total heterogeneity / total variability):   69.23%
## H^2 (total variability / sampling variability):  3.25
## 
## Test for Heterogeneity:
## Q(df = 1) = 3.2498, p-val = 0.0714
## 
## Model Results:
## 
## estimate      se     zval    pval    ci.lb    ci.ub 
##  -0.0719  0.0353  -2.0402  0.0413  -0.1410  -0.0028  * 
## 
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

Age${ }^{2}$ effect

## 
## Random-Effects Model (k = 2; tau^2 estimator: REML)
## 
##   logLik  deviance       AIC       BIC      AICc 
##   3.9813   -7.9626   -3.9626   -7.9626    8.0374   
## 
## tau^2 (estimated amount of total heterogeneity): 0 (SE = 0.0001)
## tau (square root of estimated tau^2 value):      0
## I^2 (total heterogeneity / total variability):   0.00%
## H^2 (total variability / sampling variability):  1.00
## 
## Test for Heterogeneity:
## Q(df = 1) = 0.0092, p-val = 0.9234
## 
## Model Results:
## 
## estimate      se    zval    pval    ci.lb   ci.ub 
##   0.0054  0.0037  1.4748  0.1403  -0.0018  0.0126    
## 
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

Gender effect results

## 
## Random-Effects Model (k = 2; tau^2 estimator: REML)
## 
##   logLik  deviance       AIC       BIC      AICc 
##   1.9001   -3.8003    0.1997   -3.8003   12.1997   
## 
## tau^2 (estimated amount of total heterogeneity): 0.0009 (SE = 0.0019)
## tau (square root of estimated tau^2 value):      0.0297
## I^2 (total heterogeneity / total variability):   67.29%
## H^2 (total variability / sampling variability):  3.06
## 
## Test for Heterogeneity:
## Q(df = 1) = 3.0574, p-val = 0.0804
## 
## Model Results:
## 
## estimate      se     zval    pval    ci.lb    ci.ub 
##  -0.2230  0.0256  -8.7260  <.0001  -0.2730  -0.1729  *** 
## 
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

6. Models comparison

6.1. Samples including 3 or more waves

6.2. Samples including 4 or more waves

7. Meta-analytic summary of slope estimates

Intercept-only model

ICC effect:

Fixed effect model

Age effect:

Linear model

Age effect:

Linear with gender model

Age effect:

Gender effect:

Linear with gender interaction model

Age effect:

Gender effect:

Age $\times$ Gender effect:

Quadratic model

Age effect:

Age${ }^{2}$ effect:

Quadratic with gender model

Age effect:

Age${ }^{2}$ effect:

Gender effect:

8. Identifying variance components

Age effect

Models results:

## Linear mixed model fit by REML ['lmerMod']
## Formula: B_Age ~ 1 + (1 | Domain) + (1 | Continent) + (1 | Scale) + (1 |  
##     Sample)
##    Data: re_parameters
## Control: lmerControl(optimizer = "bobyqa", optCtrl = list(maxfun = 2e+06))
## 
## REML criterion at convergence: -142.9
## 
## Scaled residuals: 
##      Min       1Q   Median       3Q      Max 
## -1.54186 -0.28655  0.07675  0.35006  1.42401 
## 
## Random effects:
##  Groups    Name        Variance  Std.Dev.
##  Sample    (Intercept) 0.0013622 0.036907
##  Domain    (Intercept) 0.0025105 0.050104
##  Continent (Intercept) 0.0003654 0.019115
##  Scale     (Intercept) 0.0000460 0.006782
##  Residual              0.0003182 0.017838
## Number of obs: 42, groups:  Sample, 26; Domain, 7; Continent, 4; Scale, 3
## 
## Fixed effects:
##             Estimate Std. Error t value
## (Intercept)  -0.1170     0.0248  -4.717

ICC results:

Plot variance components:

Figure: Variance decomposition of age effect

Gender effect

Models results:

## Linear mixed model fit by REML ['lmerMod']
## Formula: B_Gender ~ 1 + (1 | Domain) + (1 | Continent) + (1 | Scale) +  
##     (1 | Sample)
##    Data: re_parameters
## Control: lmerControl(optimizer = "bobyqa", optCtrl = list(maxfun = 2e+06))
## 
## REML criterion at convergence: -67.6
## 
## Scaled residuals: 
##      Min       1Q   Median       3Q      Max 
## -1.25858 -0.34512 -0.02312  0.36665  1.68552 
## 
## Random effects:
##  Groups    Name        Variance  Std.Dev.
##  Sample    (Intercept) 0.0091460 0.09563 
##  Domain    (Intercept) 0.0081589 0.09033 
##  Continent (Intercept) 0.0000000 0.00000 
##  Scale     (Intercept) 0.0006716 0.02592 
##  Residual              0.0025328 0.05033 
## Number of obs: 42, groups:  Sample, 26; Domain, 7; Continent, 4; Scale, 3
## 
## Fixed effects:
##             Estimate Std. Error t value
## (Intercept) -0.24404    0.04605    -5.3
## optimizer (bobyqa) convergence code: 0 (OK)
## boundary (singular) fit: see ?isSingular

ICC results:

Plot variance components:

Figure: Variance decomposition of gender effect

Age differences in risk-taking propensity: A coordinated analysis of longitudinal panels

Yunrui Liu

Alexandra Bagaïni

Madlaina Kapoor

Gayoung Son

Rui Mata

1. Overview of the project

2. Overview of panel data

2.1 Number of observations

2.2 Histogram of age distributions (all observations)

2.3 Histograms and density plots for every panel

DHS

GCOE_Japan

GCOE_USA

GLES

HILDA

HRS

LIKS

PHF

SAVE

SHARE_Austria

SHARE_Belgium

SHARE_Czech_Republic

SHARE_Denmark

SHARE_Estonia

SHARE_France

SHARE_Germany

SHARE_Israel

SHARE_Italy

SHARE_Netherlands

SHARE_Slovenia

SHARE_Spain

SHARE_Sweden

SHARE_Switzerland

SOEP

UAS

USoc

3. Multilevel model process

Intercept-only model

Fixed-effect model

Linear model

Linear with gender model

Linear with gender interaction model

Quadratic model

Quadratic with gender model

4. Multilevel model results

4.1. General risk-taking

Intercept only model

Fixed effect model

Linear model

Linear with gender model

Linear with gender interaction model

Quadratic model

Quadratic with gender model

4.2. Financial risk-taking

Intercept only model

Fixed effect model

Linear model

Linear with gender model

Linear with gender interaction model

Quadratic model

Quadratic with gender model

4.3. Driving risk-taking

Intercept only model

Fixed effect model

Linear model

Linear with gender model

Linear with gender interaction model

Quadratic model

Quadratic with gender model

4.4. Recreational risk-taking

Intercept only model

Fixed effect model

Linear model

Linear with gender model

Linear with gender interaction model

Quadratic model

Quadratic with gender model

4.5. Occupational risk-taking

Intercept only model